I fought electrical gremlins in my last suburban. Some things to check:
1. The ground from the body to the engine is notorious for going bad, easiest fix is to add a new one from the fire wall to the engine block as the original bolts to the back side of the engine.
2. The battery cables go bad. Bad crimps? Poor design? Don’t know.
I ended up replacing my OEM cables with new ac delconcables, wasn’t cheap but I DIY’d it.
I also cleaned every connection point with a brass brush and used a liberal amount of dielectric grease during reassembly.
I had also read reports of the main fuse panel in the engine bay corroding, you can pull it, Clean and grease it as well.
My suburban was a 2008 2500 model, but a lot of this applies to all suburbans those years. Good luck! In the end I traded it for a Nissan.