I think the one on the right is the a/c fan (standing in front of the car looking at the engine) because when I take out the a/c fuse it no longer comes on.

BTW, I took the car back to the second mechanic and he was trying to tell me that it is normal for the electric fan to come on when the ignition is off. Unfortunately this problem comes and goes so unless it happens when the mechanic is there they tend to think everything is OK.