Passing --arg_prefix brain_parser to the parser_eval.py should do the trick. But this requires the tagged output to be fed as input.
Here's an example where the first pass tags the words and the second pass resolves dependencies:
echo 'The quick brown fox ran over the lazy dog.' | bazel-bin/syntaxnet/parser_eval \
--input stdin \
--output stdout-conll \
--model syntaxnet/models/parsey_mcparseface/tagger-params \
--task_context syntaxnet/models/parsey_mcparseface/context.pbtxt \
--hidden_layer_sizes 64 \
--arg_prefix brain_tagger \
--graph_builder structured \
--slim_model \
--batch_size 1024 | bazel-bin/syntaxnet/parser_eval \
--input stdin-conll \
--output stdout-conll \
--hidden_layer_sizes 512,512 \
--arg_prefix brain_parser \
--graph_builder structured \
--task_context syntaxnet/models/parsey_mcparseface/context.pbtxt \
--model_path syntaxnet/models/parsey_mcparseface/parser-params \
--slim_model --batch_size 1024
This generates the following output:
1       The     _       DET     DT      _       4       det     _       _
2       quick   _       ADJ     JJ      _       4       amod    _       _
3       brown   _       ADJ     JJ      _       4       amod    _       _
4       fox     _       NOUN    NN      _       5       nsubj   _       _
5       ran     _       VERB    VBD     _       0       ROOT    _       _
6       over    _       ADP     IN      _       5       prep    _       _
7       the     _       DET     DT      _       9       det     _       _
8       lazy    _       ADJ     JJ      _       9       amod    _       _
9       dog     _       NOUN    NN      _       6       pobj    _       _
10      .       _       .       .       _       5       punct   _       _