Its common for the light bulbs to corrode in the sockets. Lights bulb case needs to be cleaned and coated with contact grease. Alum frame may not rust but will corrode. White ground trailer wire will break in insulation.

Use meter on ohms Rx1 at trailer 4 prong to see if there is electrical path. Put one lead on trailer frame and check other three for expected short.

Missed where it worked on buddies truck, does it still? Broken wire may be intermittant. With everything hooked up run temp jumper from trailer frame to truck bumper and test.

Use test light at truck 4-pin with it connected to good truck ground. Use probe in each of 3 hot holes. Some times a meter draws so little current it may read with bad connection but will not power a bulb in a test light.

I'd try the post above suggestion about using 7-pin/4-pin adapter to troubleshoot.

 

You could try and plug the trailer in the 4 way - turn the parking lights
on- take your voltmeter and put the ground wire on the truck side - then take positive lead & ***** the brown wire on trailer side to see if
you have 12 volts. repeat on other wires. if you have power on all
then take ground wire & switch to trailer ground point. if no power
then you know its the ground on trailer side. Hope this is clear &
helps- if not give us another shout & we'll start over again !!
Good Luck !!