There is a partial short in the wiring or your FSV is dying. When you start the truck, the voltage dips because of the glow system. Since the voltage is lower, the current is lower, and the fuse doesn't blow.
Disconnect the plug on the FSV. Switch between tanks, if the fuse don't blow, then the FSV is at fault, try it both ways, engine ON then OFF. Check the wires to the FSV, disturbing them might have an effect. When you switch tanks, that changes the FSV motors positive negative to change direction. See switch.