The testpoint.par file, located at /opt/rtcds/caltech/c1/target/gds/param/testpoint.par, which tells GDS processes where to find the various awgtpman processes, was completely empty. The file was there but was just 0 bytes. Apparently the awgtpman processes themselves also consult this file when starting, which means that none of the awgtpman processes would start.
This file is manipulated in the "install-daq-%" target in the RCG Makefile, ultimately being written with output from the src/epics/util/updateTestpointPar.pl script, which creates a stanza for each front-end model. Rebuilding and installing all of the models properly regenerated this file.
I have no idea what would cause this file to get truncated, but apparently this is not the first time: elog #3999. I'm submitting a bug report with CDS.