I'm pretty familiar with the door latch issue, and it's not the door latch problem. These things all go on and off at the same time, and my door latches are working fine.
Something else I noticed is if the system is acting up, then if I open my door while the engine is running, the Door Ajar light and audible alarm will both come on for only a second, then go out, even if I leave the door open. Same happens with the fasten seatbelt alarm and light, it stays on for a second, then goes out, if I unfasten my belt with the engine running.
Dash lights, running lights, daytime lights, brake lights, turn signal, radio, alarm, fans... everything else works ok.
Does this point more towards the GEM, or maybe something else?