This is what it is:

The switch you are referring to is the "roof open switch". The short version of how things work is this - the roof open switch and the cargo compartment divider switch are wired in series. When you have the divider in the trunk in the proper position, and the roof open switch is allowed to close (and it is closed as soon as you release the latch and push the top up away from the windshield frame), the two switches, together, apply a ground to pin C1-7 of the Power Top Control Module. This ground signal is part of the safety checks the system must meet before it will activate the pump.

If the switch is bad, the pump wont run - and going up or down has nothing to do with it UNLESS, somehow, the roof open switch is somehow being pressed when it should not be. It should only have pressure on it's link arm when the top is fully closed (all the way up, and latched to the windshield frame.)

It SOUNDS to me like you might have a cylinder limit switch somewhere that is sending a confusing signal to the PTCM when the top is up. The ONLY way it is the top open switch is if, somehow, there is pressure holding the actuator arm when the top is open. BUT if that is the case, how can the top travel UP and not DOWN? If it is the switch, look at the switch and see what is different about it going down versus going up. Make SURE the switch is allowed to "relax" when you unlatch the top and press the button to lower it.

If you want to measure the voltage, just know that you should see NO voltage (on, maybe .2 volts or less) on either side of the switch when the top is free of the windsheild frame. If you see 5 or more volts, there is the trouble - with no ground, the PTCM will not run the pump.

Again, the system is not as complicated as it first appears and a problem with the top open switch is easy to diagnose once you understand how the system works as a whole.