Hi Bobbie,
I had similar problems with my trailer
lights, and basically removed rust from sockets, redid splices with soder, dialectic grease and shrinkwrap, AND made sure grounds were to rust-free metal, especially the ground connection near the trailer plug.
However, as a 'plan B' back-up, in case of any future
light problems on the road, I am going to get a magnetic trailer
light kit from Harbor Freight. You pop the magnetic
lights onto your rear bumper, run the wire assembly under or over the trailer, and plug into the tow vehicle. You mentioned this idea in a previous post, so it sounds like you've seen this product before. With one of their coupons, it's only $9.99. I'd check the specs on this product to see if the wiring is long enough for the length of the trailer. If that's no issue, this kit sounds like peace of mind to me.
Good luck,
Fran