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Probably shouldn't be responding at all as I've never seen this and have a '14 SCREW so nothing I have matches your issue. Purely guessing a ground is loose somewhere; possibly corroded since you are back east and up north. I don't have a wiring diagram to refer to for your year/model so can't be of any help at all. The random-ness of it makes it feel like a loose connection in the ground. I guess it could be a hot wire somewhere also but I'd think you'd notice something not working. I'd focus in the area around the replaced light assembly and see what you can see. Some things to think about:
-Does the tailgate drop when you hit a bump? Maybe have a friend bounce the truck while you are underneath looking at stuff. You might see something moving or arcing.
-Does it drop if you change directions, going forward put in reverse and it drops?
-When the event occurs check quickly for non-working things. This might indicate it is a hot wire with insulation scuffed off.
Look for any connections and push the connectors together tighter. It might not hurt to separate them and reseat them ensuring they are tight. Hopefully you'll find something that resolves it. A much more difficult situation will be a wire that has scuffed thru the insulation and periodically grounds out causing the problem. Those can be found by working in a darkened area, I mean dark, and wiggling wires until you see a spark. I would think the ignition would have to be on unless the problem occurs with the truck parked and not moving in the driveway. I've had luck with this even though it sounds crazy. Stay focused in the area around where the light assembly was replaced or if you've had other work done or have added aftermarket items, i.e. lights, bumpers, etc.
These can be difficult problems to find and are never fun for the technician working on them. Not sure I've got anything else to offer. Be sure to update us here. It may pop up on another Forum person's truck and he or she can resolve it quickly with your feedback.
Hope you find the problem,
LZinAZ