Whoa, whoa, whoa, everyone is jumping to conclusions! No burnt wires or bad connector and jumping the black wire to body ground changes nothing. Here are the latest details (better get popcorn and a drink)...
I started again today with everything connected. Turned on parking lights and license plate lights also came on. But keyless entry (remote, FOB, whatever you want to call it) doesn't work and neither does RAP. Also, connected black wire from connector to main body ground, no difference.
I then disconnected battery. Checked continuity across each pin of connected body-to-liftgate connector and all had perfect continuity. (I had fiddled a little with the connector pins and think I fixed the loose connection I reported earlier where the plate lights would flicker. Will check again with battery connected.)
Battery still disconnected... I pulled off the liftgate interior panel (what a pain in the ass) so I now have complete access to the LGM and all liftgate wires. Pulled LGM 4-pin connector and checked continuity of each wire (orange, purple, orange, black) back to body-to-liftgate connector (liftgate side) while disconnected. All had perfect continuity (and yes, I wiggled the shit out of wires while checking). Note that the purple has perfect continuity with the black and no others. Also checked for shorts by checking each wire for continuity with each other wire (i.e. different colored wires) from one connector to the other and, as expected, there was no continuity EXCEPT I noted there was continuity with slight resistance from the purple to brown and from black to brown. For kicks and giggles I measure the resistance as ~4 ohms and ~3 ohms, respectively -- not sure what that indicates (i.e. good or bad?)
Battery still disconnected... With either the body-to-liftgate connector connected and/or the 4-pin LGM connector plugged back in it's a whole another ballgame! All kinds of strange (variable) low voltages can be measured -- remember, the batter is still DISCONNECTED. Apparently some charged circuits remain. (You guys didn't tell me about that, would be nice to know when I'm making measurements!!)
Battery connected. No longer seems to be a loose connection, couldn't duplicate flickering plate lights wiggling/pulling wires and connector. Measured the orange wires to black on the 4-pin LGM connector as advised, each measured 12V as expected. Meanwhile, still no remote operation or RAP.
Other strange phenomena and miscellaneous stuff to consider... With the meter set in sensitive settings (2V and 200 mV), I notice just waving the probes around in the air I was getting variable readings. Does this set to either DC or AC. I thought maybe the probe connections to the meter were a little loose but nope as touching them together I get a constant 0 as expected. I'm doing all this in my carport on a humid day about 50' from the nearest powerline. Been years since I last used a meter but don't remember this. Strange..........
With everything reconnected I started her up to charge for a bit since I haven't done so all week. As it warmed up and kicked down the idle I was surprised that the idle started fluctuating from ~700 RPM to ~400 RPM for a second every 5-10 seconds. Even stalled once. Hadn't been doing that. (Of course, I'm thinking at this point, "What the hell did I do now?!") I happened to turn of the heater and noticed the fluctuation immediately went away and the idle settled at 600 RPM (normal). Turned the heat on/off and idle kept fluctuating every time while on. With heat off, I tried several other items (radio, moonroof, etc.) but nothing else affected the idle.
May be worth noting that shortly before all this began (started with noticing rear wiper not working), I had a new starter installed at the shop and also jump started a car. No idea if related but I'm always skeptical of coincidences.
Okay, what next? Should I be focusing now on the LGM or the BCM? Believe me, I'd much rather find a broken wire but I haven't.