I'm not familiar with TTs but I know a little about deadbolts. Is yours one of those TriMark door locks with a built in dead bolt. If so I'll be no help at all.
I will make a suggestion, however, get rid of it and install a trimark lock with out the deadbolt and install a separate deadbolt lock. I have rebuilt my old Brinkman paddle door lock and the material used inside the assembly was not suitable for a high use mechanism of any kind. I think TriMark is the same or they had a whole bunch of defective locks.
I had a POSSE deadbolt on my rig. I hated it and wanted to install a Schlage but couldn't find a drive in bolt assembly, I really didn't look very hard and the one locksmith I did talk to didn't help at all. Then I was perusing the Schlage on-line catalog and found what I wanted and low and behold Lowe's had it in stock. You cannot remove the key from the deadbolt in the horizontal lock or unlock position. There is a center or vertical position only.
My MoHo is now keyed the same as my home and it's one less key I carry. All my keyrings for vehicles have that key on them, I can always get in either.