AMC used two setups, one with a separate wire on the ignition module - the
yellow grommet ignition module and the one with the the ECM spliced into the wires between the sensor and the ignition module - with a
blue grommet. The blue box is much more common, that's what the diagram above shows. Sorry if it was confulsing, but asking about unplugging the other connector made me wonder, the yellow box also has a third 3-pin connector that needs to be unplugged.
This is where the wiring should end up:
My understanding is that the start wire to the module retards the timing to make starting easier, but you need that plug. The other plug goes to the coil and to the sensor.
If the wiring is all clean and good, and nothing is plugged in backward then try a new module. The timing will jump around on a dying module, especially after 20-odd years.
Also, if you have advance at idle, you're on a manifold source or you have your idle set way too high. Factory setup used a ported source with no idle vacuum, but everyone had a setup at one time that used temperature switches and regulators between vacuum ports and the distributor. If you have any of that disable it until everything is working correctly.
First, I would try running with no vacuum to the distributor. Make sure it's disconnected at both ends.
Second, if it still feels like the timing is changing then look at the wiring and make sure it's correct. You may have a wire that is shorting out somewhere.
Third, I'd go get a spare box. Worst thing is you have a $25 spare part in case it goes bad. They may even be able to test your old one.