Problem solved. I experimented on my spare fob. Couldn’t figure out how to get to the back side of the button. Took the fob apart and didn’t see anyway to do it without breaking something. Then I had the bright idea to go at the button side. Using a tiny flat blade I pried up the edge of the tailgate button and worked my way around until it finally came off. Turns out it is just glued to the silicone membrane underneath.
Next step was to use a Dremel tool to grind off the tit on the bottom of the button cover. I thought that might be enough to solve the problem but it’s not. The silicone membrane has a tit inside that was activating to switch. I gently took a razor blade and cut the center out of the silicone membrane. Then it was just a matter of gluing the button cover back on.
Now the tailgate button totally disabled on the fob. No more surprise tailgate openings! I rarely haul anything and although it’s a nice feature, I can live with the button on the dash and on the gate.