To open the key fob, find the small sliding button on the back... Slide it to one side and hold it there while pulling it straight out the end as well. Tricky. Then the mechanical key will release and pull out. Leaving it pulled out about half, pull the free end up and away from the back, using it as a lever. A large part of the back will then break away... oops I mean that part of the back snaps open! There the battery is revealed. Disassembly beyond this I don't know, but two cross-head screws are seen.
When I try to hit the lock button with the fob in my pocket I have hit the funk button a number of times. Since I don't use the frunk I thought I would disable the button. The proximity sensor would still work, as would the lever by the door sill. Just a thought.