Where do Alzheimer's patients "hide" things?

LOL Sorry, but your question struck me as funny, ALZ people don't belong to a secret society with rules!
Might they have a safe deposit box? My parents kept papers in shoe boxes in the attic... a bedroom drawer? top closet shelf? in a suitcase?
Each family has their own clever hiding spots, when I was moving my mom I found a forgotten wad of cash hidden in the studs in an unfinished corner of her bedroom closet. If things can not be found you will have to go through the process of replacing them, just as people must who have had a fire or flood, laborious but doable.

The papers could be anywhere, but my cousin, who has dementia, had her papers in a safe box inside her home. It was pretty easy to get to and she had told me years earlier where they were, however, she had hidden the cable box in the kitchen cabinet and that took me hours to find.

If you need the title quickly, I'd get a duplicate from the Department of Motor Vehicles. They charge a hefty fee in my state, but, it's worth it, if it's going to take many hours to locate. I would continue to try to find the other items though, because if you need them later, you'll have to pay a lot to get copies.

And, I would look at mom's driving. Is she okay to drive?

Also, I would start to prepare to get all new Power of Attorney, Wills, etc. ASAP. Is dad still competent to sign them?