Assuming a new ish 5th gen Ram I'd probably suspect the camper, not the truck, to be honest.
Can you verify the pin out of either the 4 or 7 way connection using a voltmeter to confirm there is 12V being supplied to the camper for the running lights?
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Fuses are listed in tabular form on page 394 of my Owner's Manual for my '21 Big Horn, perhaps they are in yours as well. The ones associated with towing lights are F08 through F12, located in the External Power Distribution Center, left side engine bay looking forward, near the battery.
I would guess the running lamps are a cartridge fuse, F12, but it'd depend on your truck.
![Screenshot from 2023-11-01 10-39-28.png Screenshot from 2023-11-01 10-39-28.png](https://5thgenrams.com/community/data/attachments/170/170314-b57fd201909f02072390f1e1c3b30618.jpg)