Do It Right The First Time !
x3 on soldered connections.
A single ground wire down both sides of the trailer connected into one wire at the front, will work, as long as all joints at the lights are soldered, cleaned, and heat shrink with adhesive is used to seal them.
All the soldered connection should be cleaned and covered with Heat Shrink... yes, but use the Heat Shrink with adhesive inside of it, once you shrink it you will see the adhesive come out the ends and seal the joint... no corrosion, no dirt, a good connection for a long time.
Don't let where you buy the Heat Shrink tell you the regular heat shrink will keep dirt and moisture out of the connection, it won't... ALWAYS use the adhesive type of heat shrink only !
As I have said earlier, I have rewired a number of trailers for friends, replaced all of the lighting with waterproof LED Lights, and soldered all connections with the adhesive type os heat shrink. All o the trailers I rewire are still running the new lighting, some after as long as seven years.
Good Luck but as I opened this post, "Do It Right The First Time" !