For a car in storage in a tropical environment, do brake pads
deteriorate over time due to humidity? If so then what about the
shelf life of brake pads at the auto parts store?

Or is it only when having been parked in standing water that the pads
start to deteriorate? If one merely drives thru puddles, the heat of
having driven drives the water off?

For long-term storage, one wants to give the engine exercise once a
month, else it will gum up or something, I hear. Brakes pads need
exercise too?