Well, after tracing every wire in the thing, taking most of it back apart... I'm fairly sure I located the issue.

At the same time I did a number of other more invasive upgrades I plugged in one of the British Atlantic trailer hitch light kits. It didn't cross my mind that the sealed, plug and play, module could be at fault... but when I removed it the voltage on the back-side of the constant-power fuse (the one that runs the clock etc) dropped from 1.5V to .05V which to me would indicate that it was shorting something.

I'm going to go put enough back together now to do a test drive and see if the problem returns at all.