Got it taken care of already.
The voltage on the 12V rail was hovering around 11 - too low for the M2 to supply power. The ticking/clicking may have been a relay firing, or it was some power switching on and off, I'm not sure.
In case anyone else has the problem, the solution was to put a load on the 5V rail with a disc drive or any other peripheral. That, for whatever reason, boosted the voltage on the 12V rail.
The other solution is to get a better power supply that doesn't exhibit these quirks