How to replace a tail light in a 1989 Chrysler new yorker?

Your 89 New Yorker has a peice of trim at the bottom the tail light, in that small piece of trim is a screw. Take that screw out and you can get to the rest of the screws that hold the tail light assembly in place, Oh yes most important you must have the trunk lid raised so you can get to the wiring harness.