I’m not banking on the 4-way as the problem for your taillights not working because it could have been caused by the ground tabs in the sockets. And it could possibly be a case of the 4 taillights’ unified electrical pulses/surge tickling the ground contact enough to jump a ground connection. After all, the failure is a textbook example of bad ground tabs.

The switch may be full of crud or whatever makes it lock is gummed up. Maybe use some wd-40 with a squirt tube attached; squirt some into the switch the best that you can, and work it in and out.

It’s not that I’m a big fan of wd-40 as penetrating-type oil. The thing is that it’s safe to saturate switches with wd-40 because water displacement, formula #40 was specifically designed to displace water from electrical components.