This is my right rear side marker socket. It's the same shape as the other rear marker but the side conductor doesnt touch the contact on the side of the bulb. This is the bulb that's in both of them now:
Bayonet based #1895, for socket you have, it's the correct bulb... These bulbs & #1891 were common till late '60s, replaced by wedge based #194...
In those sockets usually there is a metal sleeve that bulb fits into, then twists to lock... I've seen a few cheap plastic sockets with just a side contact, but never in a OEM application...
There's about 1mm of a gap between the nub on the bulb and the side contact when it's fully seated in the socket. Almost like the bulb is too small for the socket. The other one works fine, but the side contact in it is different. Its spring-loaded toward the bulb. When you twist the bulb in, it makes contact with the nub.
I just find it annoying that the last guy didn't bother to check if the socket matched the old one or even worked.