It looks like I've figured out one part of the equation to make this easier, although I'm not sure if it's going to work with the upfitter buttons since they are not momentary.
It looks like this is properly setup with two relays and a timer that when it receives a key on signal it starts the timer to open the cutout, and then once the timer ends it closes the cutout. It looks to also have a momentary button to manually override the timer that one press opens the cutout, and then a second press would close the cutout. I feel like this is a much simpler solution than trying to use separate timers and relays with the aux switches.