An owner of a 2002 caravan reports a resistance of 10K when no pinch is detected, and a resistance of close to 0 ohms (short) when a pinch condition is detected.
https://www.justanswer.com/dodge/7vhxr-dodge-caravan-2002-power-rear-liftgate.html
It also sounds like a DRBIII would be very helpful for diagnosing (not to say that you can't figure it out otherwise though) as it could instantly give you all the sensor/switch readings.
"The power liftgate system was designed to be diagnosed with an appropriate diagnostic scan tool, such as the DRB III®. The most reliable, efficient, and accurate means to diagnose the power liftgate system requires the use of a DRB III® scan tool and the proper Body Diagnostic Procedures manual. The DRB III® can be used to observe various switch statuses throughout the power liftgate system to help the technician diagnose a defective switch or component. The DRB III® can also be used to actuate various components throughout the power liftgate system to help the technician diagnose a defective component."
For a 2009, but maybe still pertinent:
ftp://oskin.ru/pub/chrysler-dodge/m.../manuals/Service Manuals/2008-2009_RT_Town&Country_Caravan_Voyager/liftgate.pdf
"If a liftgate pinch sensor is activated during a power close, the liftgate will reverse direction. If a pinch
sensor is already active the power liftgate will not initiate a power close. A pinch activation during latch
cinch will stop the cinch operation."
"Pinch sensor reads 10K ohms when not pinched. When pinched, shorts out the 10K ohm resistor and should read from 0 to approximately 200 ohms."
"DRIVE CLUTCH Provides + 12 V to clutch in power liftgate drive unit to engage drive mechanism for power open or close"
So maybe you can check voltage on the drive clutch to see if the motor clutch is active and preventing you from manually lowering it? That might provide a clue as well.