Helping friends with utility trailer lights, I have run across some where the bulb(s) is manufactured as part of the
light and the whole thing is replaced as a unit.
If several lights aren't working, then it's likely the wiring, and if it's the wiring, it's likely the ground/return wires.
Darwin is right on about
LED lights because they will draw far less current and not create TV current problems, esp if your trailer lights are just tapped into the TV lights and not on a tow-package relay.