Blower motor runs when doors are unlocked with key fob?

 

Should be no relation between those two circuits, unless you have some kind of remote climate start feature. My 2006 is a work truck model, so it certainly didn't (manual everything on that truck!).

I would be tempted to say this is something to do with the BCM (body control module), as it is involved with the locks, but I do not think it is tied into the HVAC system at all.

You may want to try and decipher the wiring diagrams on charm.li and see if you can figure something out...