Hello and welcome to JustAnswer!
This is very likely a bad relciner motor. if you hear the click from the module under the seat that tells me that the switch is ok and the module is sending power to the motor but the motor won't move. I've done a hanful of these. The recliner motor is in the seatback itself, but not terribly hard to replace. The first thing to do would be to pull the trim off the back of the seat and check for power and ground at the recliner motor while a helper pushes the switch. If it has power and ground and won't move it will need to be replaced.
does the trim just snap off on the back of the seat or is there a trick to pull it off?
where would I buy the motor and what kind of motor would I ask for?
You'll have to get the motor from a dealer parts department. Ask for the recliner motor.
The panel on the back of the seat is held on by hooks. From the top, use a prying tool, pry down and towards the rear and disengage the hook that goes across the top. Then you can pull the panel straight up and off the seat.