No it doesn't make sense. However, all true design military vehicles such as the M35, M37, etc... Have wierd things happen if a ground is not good. Take the 4 bulb bucket tail lights on your 101. If you unplug all but one light power wire. Then undo the ground bolts at the back. Chances are a light that isn't even plugged in will light up when you apply power to the one wire left hooked up. I know it doesn't make sense. I also know I have had this happen when making wiring harnesses for my M715 and my Gasser M35. Weird things happen to MV's when the ground isn't right. Un bolt your lights, clean the bolts and bolt them back up since that is your ground. Do you have the plastic light buckets? Only one of those bolts is the ground and it can come loose from the grounding strap inside the bucket. Start there.
If your plug on the bumper test out like the listing I posted. Then you probably do have a problem on the trailer. Un plug the lights and then pull the cover off the pig tail to trailer connections. Unplug the pig tail. Then using your ohm meter, verify that each wire at the front of the trailer actually goes to where it is supposed to on the back. Plug things at the light buckets back up as you test each wire. Now, plug the pig tail into the truck with it still not plugged into the trailer. Test everything for power at the proper wire number. If every thing checks out, start connecting the pig tail back to the trailer one wire at a time. Test each one for working lights before you move on. If everything works great until the last wire gets plugged in and then everything goes stupid again. Unbolt the light buckets from the trailer, remove the bent metal hanger for the lights, clean everything and put it back together with star washers on the 3/8" bolt holding the buckets to the holders.