I have a 2004 Chev Suburban and my trailer running lights do not work but the stop and singnal lights do. Can this be a fuse issue and if so what fuse runs the running lights?

does the 3rd brake light in the back window work? check fuses if fuses are OK and the hazard lights work, then the turn signal switch may be bad. I dont know what your sons suburban (trailer?)has to do with your navigator?

20 amp

First check turn signal fuse. If it is good most likely the turn signal flasher needs to be replaced.

your truck has a different set of fuses for the trailer. They are located in the electrical center under the hood on the drivers side fender well.

Did you check the fuse for the trailer tow adapter paring lamps ? This is a separate fuse powered by a relay, it is not the same circuit as the truck's parking lamps.
This is fuse # F10 & The half size ISO relay, R201 in the fuse panel in the passenger side kick panel.
This is based upon being a new body style 2004, not the 2004 Heritage or Lightning models, those are different fuse & relay locations.

Check owners manual. Check under hood fuse panel. Likely a blank spot where needs to be added.

You can pick up a 97 Chev Silverado Haynes mechanics manual. It has all the electrical diagrams towards the back of the book. Canadian Tire has them you may be able to get one off of ebay maybe Amazon.

My 2004 f150 has the factory tow package. It has a fuse for the trailer running lights seperate from the truck running light fuse.
Check, you may have the same set up...

The fuses and relays for the trailer are isolated from the regular running lights, I believe the fuses and relays are in the underhood power ditribution box.