Fuze box has a circuit board inside it that corrodes. Parking lights staying on is the thing to malfunction.. common issue that year.
read this thread: https://dodgeforum.com/forum/3rd-gen...s-stay-on.html

 

Just joining the forum and had done a search for just this problem. Pulling fuse #33 had no effect in turning off the tail/park lights, but pulling #1 fixed the problem. That's the relay for trailer brake and trailer battery!!

I had seen a post on YouTube where someone clipped the wires to the trailer connection and eliminated the problem. Apparently there is some sort of problem with grounding??

Hope this helps someone else!!

 

My parking lights on 04 Ram 1500 were staying on when parked and truck off I replaced the FCM, I checked the trailer light socket for corrosion I toggled the light switch many times I replaced the relay in the fuse box which I could hear clicking no change the lights stayed on but flickered when it clicked so I bought electrical cleaner spayed it on the relay connection points in the fuse box put the relay in and out many times over then sprayed and repeated putting the relay in and out all while the battery was disconnected then used compressed air to clean and dry and so far seems to have worked the lights are off and the relay is not clicking so I'm thinking a poor contact in the fuse box. Will see if this was the fix.

 

I pulled my 40 amp trailer fuse out that’s located under the hood. Solved the problem.

 

Have a look at where the trailer harness hits the main harness, not always the best splices there.....