The traditional tool for comparing time stamps to determine whether work needs to be performed or not is make. Its default behavior is to calculate a dependency chain for the specified target(s) and determine whether any of the dependent files have changed; if not, the target does not need to be remade. This is a great tool for avoiding recompilation, but it easily extends to other tasks.
In concrete terms, you'd create a flag file (say, .made) and specify it as dependent on your file. Now, if file has changed, .made needs to be recreated, and so make will run the commands you specify to do so. In this scenario, we would run a simple piece of shell script, then touch .made to communicate the latest (successful) run time to future runs.
What remains is for the recipe to run different commands at different times. My approach to that would be a simple case statement. Notice that make interprets dollar signs, so we need to double those dollar signs which should be passed through to the shell.
.made: file
case $$(date +%H:%M) in \
09:* | 10:* | 11:[0-2]? ) \
scriptA.sh ;; \
11:[3-5]? | 1[2-6]:* | 17:[0-3]? | 17:4[0-5]) \
scriptB.sh;; \
17:4[6-9] | 17:5? | 1[89]:* | 2?:* | 0[0-8]:* ) \
scriptC.sh;; \
esac
touch $@ # $@ expands to the current target
The entire case statement needs to be passed as a single logical line to the shell, so we end up with those pesky backslashes to escape the newlines.
Also notice that make is picky about indentation; each (logical) line in the recipe should be preceded by a literal tab character.
The default behavior of make is to run the first target in the file; this Makefile only contains one target, so make is equivalent to make .made.
Also notice that make cares about exit codes; if scriptA, scriptB, or scriptC could exit with a non-zero exit status, that is regarded by make as a fatal error, and the .made file will not be updated. (You can easily guard against this, though.)