Not being to tell what color fluid is in your picture, I'd say it's either front lip seal on the transmission or rear main seal on the engine.
On the tire question. Not saying this is the problem, but the dealer is correct. Different diameter tires on the front verses the rear can make the transfer case bind up and jump out of gear. You can test this theory by interchanging two of the tires front to rear on one side of the truck. If the jumping stops, you found your problem. Hope this helps.
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Wednesday, September 2nd, 2020 AT 10:32 AM