Strange, I have a 97 JDM with keyless entry and a remote and the door buttons go up and down when you press the remote. When I unplug the box shown in my picture the keyless entry no longer works. Not sure if this is After market installation but the Key Fob has an Isuzu badge on it.
The wiring for the Box disappears into the drivers side door pillar and also under the dash so I will have to see if I can remove it and transfer it to my registered JDM. Looking at the wiring it doesn't seem to be bound in with other harnesses under the drivers seat so I am thinking it maybe be an aftermarket install. I also note that if you google the part number 619431-0050 show on the picture that the results show a Toyota Keyless entry box.
Before I got to the trouble, I will check the doors on both vehicles to see if the solenoids need to be moved as well.