I made GNU Make's grammar for myself, you can find the grammar and overview of lexer below. It's not perfect, but it can serve as a starting point for someone who wants something better. Some additional and background information is in the post.
Implementation: lexer and parser.
Bison's dump of the grammar
/* Assign lower precedence to NL. */
/* %precedence NL */
/* %precedence COMMENT "ifdef" "ifndef" "ifeq" "ifneq" */
  1  makefile: statements "end of file"
  2          | "end of file"
  3  statements: br
  4            | statement
  5            | statements br
  6            | statements statement
  7  conditional: if_eq_kw condition statements_opt "endif" comment_opt br
  8             | if_eq_kw condition statements_opt "else" statements_opt "endif" comment_opt br
  9             | if_eq_kw condition statements_opt "else" conditional
 10             | if_def_kw identifier statements_opt "endif" comment_opt br
 11             | if_def_kw identifier statements_opt "else" statements_opt "endif" comment_opt br
 12             | if_def_kw identifier statements_opt "else" conditional
 13  conditional_in_recipe: if_eq_kw condition recipes_opt "endif" comment_opt
 14                       | if_eq_kw condition recipes_opt "else" recipes_opt "endif" comment_opt
 15                       | if_eq_kw condition recipes_opt "else" conditional_in_recipe
 16                       | if_def_kw identifier recipes_opt "endif" comment_opt
 17                       | if_def_kw identifier recipes_opt "else" recipes_opt "endif" comment_opt
 18                       | if_def_kw identifier recipes_opt "else" conditional_in_recipe
 19  condition: '(' expressions_opt ',' expressions_opt ')'
 20           | SLIT SLIT
 21  define: "define" pattern definition "endef" br
 22        | specifiers "define" pattern definition "endef" br
 23        | "define" pattern ASSIGN_OP definition "endef" br
 24        | specifiers "define" pattern ASSIGN_OP definition "endef" br
 25  definition: comment_opt br
 26            | comment_opt br exprs_in_def br
 27  include: "include" expressions br
 28  statements_opt: comment_opt br
 29                | comment_opt br statements
 30  if_def_kw: "ifdef"
 31           | "ifndef"
 32  if_eq_kw: "ifeq"
 33          | "ifneq"
 34  statement: COMMENT
 35           | assignment br
 36           | function br
 37           | rule
 38           | conditional
 39           | define
 40           | include
 41           | export br
 42  export: "export"
 43        | "unexport"
 44        | assignment_prefix
 45        | assignment_prefix WS targets
 46  assignment: pattern ASSIGN_OP comment_opt
 47            | pattern ASSIGN_OP exprs_in_assign comment_opt
 48            | assignment_prefix ASSIGN_OP comment_opt
 49            | assignment_prefix ASSIGN_OP exprs_in_assign comment_opt
 50  assignment_prefix: specifiers pattern
 51  specifiers: "override"
 52            | "export"
 53            | "unexport"
 54            | "override" "export"
 55            | "export" "override"
 56            | "undefine"
 57            | "override" "undefine"
 58            | "undefine" "override"
 59  expressions_opt: %empty
 60                 | expressions
 61  expressions: expression
 62             | expressions WS expression
 63  exprs_nested: expr_nested
 64              | exprs_nested WS expr_nested
 65  exprs_in_assign: expr_in_assign
 66                 | exprs_in_assign WS expr_in_assign
 67  exprs_in_def: first_expr_in_def
 68              | br
 69              | br first_expr_in_def
 70              | exprs_in_def br
 71              | exprs_in_def WS expr_in_recipe
 72              | exprs_in_def br first_expr_in_def
 73  first_expr_in_def: char_in_def expr_in_recipe
 74                   | function expr_in_recipe
 75                   | char_in_def
 76                   | function
 77  exprs_in_recipe: expr_in_recipe
 78                 | exprs_in_recipe WS expr_in_recipe
 79  expression: expression_text
 80            | expression_function
 81  expr_nested: expr_text_nested
 82             | expr_func_nested
 83  expr_in_assign: expr_text_in_assign
 84                | expr_func_in_assign
 85  expr_in_recipe: expr_text_in_recipe
 86                | expr_func_in_recipe
 87  expression_text: text
 88                 | expression_function text
 89  expr_text_nested: text_nested
 90                  | expr_func_nested text_nested
 91  expr_text_in_assign: text_in_assign
 92                     | expr_func_in_assign text_in_assign
 93  expr_text_in_recipe: text_in_recipe
 94                     | expr_func_in_recipe text_in_recipe
 95  expression_function: function
 96                     | '(' exprs_nested ')'
 97                     | expression_text function
 98                     | expression_function function
 99  expr_func_nested: function
100                  | '(' exprs_nested ')'
101                  | expr_func_nested function
102                  | expr_text_nested function
103  expr_func_in_assign: function
104                     | expr_func_in_assign function
105                     | expr_text_in_assign function
106  expr_func_in_recipe: function
107                     | expr_func_in_recipe function
108                     | expr_text_in_recipe function
109  function: VAR
110          | "$(" function_name ")"
111          | "$(" function_name WS arguments ")"
112          | "$(" function_name ',' arguments ")"
113          | "$(" function_name ':' expressions ")"
114          | "$(" function_name ASSIGN_OP expressions ")"
115  function_name: function_name_text
116               | function_name_function
117  function_name_text: function_name_piece
118                    | function_name_function function_name_piece
119  function_name_piece: CHARS
120                     | function_name_piece CHARS
121  function_name_function: function
122                        | function_name_text function
123  arguments: %empty
124           | argument
125           | arguments ','
126           | arguments ',' argument
127  argument: expressions
128  rule: targets colon prerequisites NL
129      | targets colon prerequisites recipes NL
130      | targets colon assignment NL
131  target: pattern
132  pattern: pattern_text
133         | pattern_function
134  pattern_text: identifier
135              | pattern_function identifier
136  pattern_function: function
137                  | pattern_text function
138                  | pattern_function function
139  prerequisites: %empty
140               | targets
141  targets: target
142         | targets WS target
143  recipes: recipe
144         | recipes recipe
145  recipes_opt: comment_opt NL
146             | comment_opt recipes NL
147  recipe: LEADING_TAB exprs_in_recipe
148        | NL conditional_in_recipe
149        | NL COMMENT
150  identifier: CHARS
151            | ','
152            | '('
153            | ')'
154            | identifier CHARS
155            | identifier keywords
156            | identifier ','
157            | identifier '('
158            | identifier ')'
159  text: char
160      | text char
161  text_nested: char_nested
162             | text_nested char_nested
163  text_in_assign: char_in_assign
164                | text_in_assign char_in_assign
165  text_in_recipe: char_in_recipe
166                | text_in_recipe char_in_recipe
167  char: CHARS
168      | SLIT
169      | ASSIGN_OP
170      | ':'
171  char_nested: char
172             | ','
173  char_in_assign: char_nested
174                | '('
175                | ')'
176                | keywords
177  char_in_def: char
178             | '('
179             | ')'
180             | ','
181             | COMMENT
182             | "include"
183             | "override"
184             | "export"
185             | "unexport"
186             | "ifdef"
187             | "ifndef"
188             | "ifeq"
189             | "ifneq"
190             | "else"
191             | "endif"
192             | "define"
193             | "undefine"
194  char_in_recipe: char_in_assign
195                | COMMENT
196  keywords: "include"
197          | "override"
198          | "export"
199          | "unexport"
200          | "ifdef"
201          | "ifndef"
202          | "ifeq"
203          | "ifneq"
204          | "else"
205          | "endif"
206          | "define"
207          | "endef"
208          | "undefine"
209  br: NL
210    | LEADING_TAB
211  colon: ':'
212       | ':' ':'
213  comment_opt: %empty
214             | COMMENT
Some lexer details
- All in 
' and almost all in " quotes are literals. 
')' ::= <unpaired )> 
'}' ::= <unpaired }> 
"$(" ::= "$(" | "${" – beginning of an expansion 
")" ::= ")" | "}" – ending of an expansion 
"end of file" ::= <end of file> 
COMMENT ::= <# comment (can be multiline)> 
ASSIGN_OP ::= "=" | "?=" | ":=" | "::=" | "+=" | "!=" 
CHARS ::= <sequence of non-whitespace> 
WS ::= <sequence of whitespace> 
NL ::= "\n" | "\r" | "\r\n" 
VAR ::= /\$./ 
SLIT ::= <single- or double-quote literal> 
LEADING_TAB ::= <tabulation at the first position in a line (eats NL)> 
Whitespace handling is tricky: lexer should ignore it unless previously
returned token needs that whitespace after it.
Unpaired closing parts of expansions () or }) are just themselves.
While contents of $(...) or ${...} is never a keyword.
Addressing confusion
Two comments express the same question:
On the other hand thou make somehow does parse the makefiles and allows some and rejects others...
You don't need a grammar to parse a languages. However, it's a nice thing to have.
In general, there are more possible languages than there are formal grammars, because grammars have constraints which exclude some languages.
I guess that make reads input and processes it at the same time while managing state, such that at every point it knows what kind of input it can accept next and what to do with it. Formal languages lean to being context-free, which means that they don't keep much record about their state. It's this gap, which makes it hard to formalize make's language, even though implementing it without a grammar is still possible.