Yes, that looks like a fan switch, and yes they are somewhat troublesome. use a short piece of wire to connect those two wires, bypassing the switch to see if the fan moves, better yet, check the voltage on both wires with a multimeter to see if it stops on one side or if both sides have some voltage. Then move to the voltage supply if there's no voltage at either, or the fan if there is voltage at both.
That switch is probably a resistor to have two speeds, that's why they tend to fail. High speed is connecting the wires directly, low speed is a resistor between the in and out.