Your ZJ has door modules, which are the switches on the LF and RF doors, but are more complicated than regular switches. It sounds to me as if the passenger door module is not communicating over the BUS system. The passenger side module handles the keyless entry, the passenger windows, mirror, etc.
It can be tough to diagnose without a scan tool, but if you can trade that driver's door module you bought for a passenger side module, try it. Even if it works, you'll have to have your remotes re-coded to the new module before the keyless entry system works.