It is in need of a lot of repairs due to several roof leaks and sitting vacant in the hot and humid Florida sun.

Once glued down they cannot expand/contract in temperature or humidity changes

I would tsp-> sand -> oil prime -> 2 or 3 light coats on that vanity just because it last a humid room.

Tough year after year of exact same temp everyday. 85 and humid.

Besides.. it's much more humid in Louisiana.  

I've had great tenants in rentals that don't include central AC, but here in North Carolina with our 100-degree + high humidity summers, it's almost a certainty that every household will run AC most days from the end of the school year through the end of September. 

For mold to grow you need a source of water and a nice humid place to let the mold grow.Tear out the drywall, let everything air out with fans, and then replace any water damaged items and you'll be fine.

I believe the humidity it bringing out the smell that has seeped into the subfloor and perhaps the joists.

This is easier to maintain than messing with paint due to high moisture / humidity issues. 

I used to do REO rehabs for FHA and most homes that had not been occupied in a while had mold due to water and temperature / humidity extremes.