Sure! Take the bezel off the trailer. There is probably a few inches of excess wire inside. You could just pull on it but until you know the condition behind the fixture I would remove it and look. You can either splice the wire and leave it behind the light or pull out a couple of inches so you can wire nut to it.
When installing a wire not turn the nut clockwise until it twist the second wire around the main wire about two times and it will be tight enough. I would then go buy some scotch 130 tape (rubber tape and wrap it all up stretching the tape, follow up with at least three full wraps of scotch 33 or 88 tape. There is also a
tape that can be used as a first wrap.
This will give you a better longer lasting connection than a crimped connection unless you have a set of calibrated