Found the problem today.
Tore into the liftgate. Removed the lower trim on the inside of the lifgate, which reveals the connector for the wiring that supplies the things inside the rear handle (liftgate release, license plate lights, and backup camera).
The new cheapo Amazon liftgate switch I got was the wrong one as it contains no wiring for the backup camera. But I was able to use it for diagnosis. I unplugged the existing wiring and plugged in the cheapo Amazon unit and the liftgate release on the cheapo Amazon unit worked fine.
So then I used my multimeter between the existing wiring connector and the wiring for the liftgate release, and there was no continuity on one of the wires.
This is what that correct harness looks like:
Due to the Covid-19 outbreak LR Centre are experiencing certain supply issues and are unable to offer these items on our usual 1-2 working day order time. We expect any orders for these parts to take at least a couple of weeks to fulfil although we can not be sure due to current uncertainties
www.lrparts.net
That's about $280. Once I saw that price, I knew I was just replacing those wires on my existing harness.
Easiest way to get to the existing harness is to just remove the entire liftgate handle. Did that and replaced the two liftgate wires. Could easily tell which one was the bad one as I could see a break in the wire once I pulled it out of the loom. Not exactly sure why it went bad as I've never messed with this wiring before, have never been in an accident, never had a problem with the rear liftgate before, etc. But the wiring for the liftgate is very thin and very brittle, so who knows.
Tested it a bit without putting anything back together and it works fine. Buttoned it all back up and it still works fine.