The symptoms you describe would indicate that the electrical portion of your rear wiper system is working. It's likely there is an internal failure of a mechanical component of the wiper motor.
Consider to check out various sources of this motor assembly. Ensure that you are getting the entire assembly, including the gearbox, as you have reason to believe (whirring sound) that the motor is running. Examine the photos of the sources you discover to note bolt placement and wiring, which would also have a connector on the wiring.
The trickiest part, in my experience and opinion, is going to be removing the body panels from inside the vehicle. It's not tricky, it's only the trickiest part. Sometimes the plastic rivets used to hold the panels in place will break before they release, which then requires to purchase new ones.
You can consider also to purchase an inexpensive (harbor freight?) panel release lever set to assist the process.
Once the panel is removed, you should be able to see the fasteners for the wiper motor, as well as the matching connectors.
Prior to all this, also consider to examine the fastener of the wiper shaft to the vehicle. It may be a threaded collar that slides off after you remove the wiper arm. This is the last point of removal, as you want the collar to hold everything steady while you are working in the panel area.