Yes it "could" be a bad switch.
It "could" also be:
Some testing with a Volt-Ohm meter (VOM) could narrow this down.
A resistance check of the motor windings would be a good first test. Or run the motor directly from battery to confirm that the motor works.
At the very least consider performing a visual inspection before replacing the switch as it's an expensive part to replace on a guess.
OBTW; it might be handy to mention the model year of your Mustang. Why? Because many model year mustangs the windows are protected by auto resetting circuit breakers.