I'm in Connecticut/New England.
I'm in Maine so I'm close but not that close. I would HIGHLY recommend dropping the spare while you're at the dealer.
1) You will know if the jack and tire removal hardware is still in the vehicle
2) You'll know if the mechanism if frozen, which is common in the northeast and why people leave the spare in the bed of their trucks
3) You'll be able to see what's going on for corrosion on the rear crossmember and other rear frame sections.
It's super easy to do and there's no reason why a dealer would object to something like this, especially on an older vehicle.