I have major problems with this. Every car I have bought in the last few years will not allow the FOB to be locked in the car. The locks simply wont engage. I don't have the push button proximity system either. It just knows that the FOB is in the car. I wish there was a way to take the FOB on the dive but I have experimented with several underwater rated boxes and every one has leaked if you're doing even a semi deep dive. I have had to hide them around the car somewhere and hope that no one finds them. I would love to hear what people with this problem do. I don't know if the hitch would be too close.
A receiver hitch safe would work. Proximity keys have to be within a couple of feet of the ignition for them to pick up the RF signal from the key. They work like those little stickers they put on merchandise in stores. You walk by the antenna on your way out of the store and if the metal in the sticker hasn't been deactivated at the register the alarm goes off. If the ignition can't receive the signal from the key it won't start the car.
When I was a cop we had a problem with lost keys or officers forgetting and taking the only chip key (proximity key) home after their shift. A dumb key wouldn't start the car only unlock the doors. Was costing lots of money to have new chip keys made every few weeks when one got lost.
What we ended up doing was taking the chip key and duct taping it under the steering column. Left it there permanently. The car thought the chip key was in the ignition because it was close enough to receive the signal from the key, so we could use the dumb key to unlock and start and drive the car. If the officer took his key home or lost it, no problem, we just cut another dumb key, cost 40 cents.
The proximity key doesn't have to actually be *in* the ignition, it just has to be within a couple of feet of it.
You might try getting one of those lead-lined camera film bags on ebay. Once you put your fob in there, the lead lining would block the signal from the fob and your car wouldn't know the fob was inside the vehicle.
On my 2016 Ford F150 I can leave the keys (with fob) in the truck, even in the ignition, and lock the doors manually by pushing the lock button on the door down. I do that when it's hot outside and I have my dog in the truck and need to go inside a store for a few minutes and I want to leave the motor running so the AC stays on. Yours might work the same. The fob might not lock the doors but you might be able to lock them manually.