Maintenance man icon waving at you?

Can't beat the CJ2 diagnostics capability. It could be the head unit or even both actuators. Easy enough. I'd go for the right (passenger side) actuator since it is easier to access although still a PITA.

Pull the temp actuator electrical connector and look for the 4-5 volts that comes from the climate control head unit. If missing it is the head unit, otherwise one or both actuators.
If you need the GM FSM auto climate control system (ACC) diagnostics I have it on PDF file.