While there are adapters for most combinations, luck has it that the one you have won't be the right one or the connector on the trailer won't be wired correctly.
What I did was buy an inexpensive set of Magnetic Tow Lights
at Harbor Freight and take those with me when I go look a a trailer. If the connector fits, that's fine, if not I just string the wires to the back and attach the magnetic bases to the rear bumper and secure everything with wire ties. But this won't work on trailers with fiberglass
covered bumpers, but you can use some duct take to hold them in place on those.
Costs less than $20 and you are prepared for any occasion.