My '21 P1000 SE was delivered with the remote plug inside the glove box as you mentioned. This is a compromise that allows winch operation while in the vehicle and while out front guiding the rope back onto the drum. However, the wire length is only enough to get to the front of the vehicle. I added a wireless remote ($20 on Amazon):
winch remote
I use it more than the wired remote. I added a "kill" switch on the dash which removes power from the remote receiver, otherwise it would be always on, and since the winch is factory wired to the battery through the contactor (relay) stray RF might cause the winch to operate uncommanded and that could break things. The winch can still be operated power off, though if the engine is available, that will help prevent depleting batteries (I added a AUX bat and changed the winch wiring to AUX.