I hear a faint clicking or ticking sound coming from inside my walls, what is it?

The sound of a very faint clicking or ticking sound is more than likely some sort of bug. More than likely it is bees, carpenter bees or wasps. It also could be carpenter ants. I would go outside during mid day and observe around the area of your house where the sound was originating, and if it's bees or wasps you should be able to see them going into the hole to the inside of your house.

I would then get a dust bee killer like Delta Dust Multi Use Pest Control Insecticide and at dusk when all the bees or wasps have gone inside, dust the entry way using a Powder Duster with Extension Nozzle.  The bees will track the dust inside the nest and eventually kill the hive.  Once all the bees are killed be sure to seal up the entry hole with caulk.