I bought replacement lamps for my refrigerator. Both bulbs are new
and I tested them with a continuity tester to verify them. Neither
bulb works in either socket. I also tested the center pin inside the
fridge and it is hot (and will go off when I push the door switch).

Without taking the thing down, I can't see into the sockets. One
thing I noticed is the shell connections are plastic. There must be a
metal pin inside that touches the shell at some point, but I don't see
one. I gave the bulbs a pretty strong twist when I put them in. I
twisted tighter than I normally would have even tried, but neither
bulb will glow.

The fix has to be twist tighter, but I really really made them tight
the first time. Anyone else have this problem?

My fridge is a 15 year old Kenmore.