OK here's a stock picture of the connector (not mine)
https://jshare.johnshopkins.edu/cfranck1/connector.jpg
The white locking bar came out a while ago but this never caused any problems. I don't know if it's supposed to be detachable or not. What came off is the beige part, which fits over two metal tabs sticking up from solder patches approx. where the green highlights are. After trying to reattach everything, the tabs broke and are now inside the connector.
Is that whole thing, under normal circumstances, physically secured only by those two tabs? As it's holding together now, those two areas are definitely contacting the connector, so I'm not sure why the trackpad wouldn't work.
Anyway, now that I've given about as much detail as I can, would soldering be a fairly risk free way to repair this?