Ok, we are both wrong. It will take me some time (a few days) to put it all together, but I just printed the entire chapter (starting on page 23-454 and going to 23-482) on the Top System.

Here is how it goes:

1) You reach up and turn the handle to release the top from the windshield frame. This causes the "Latch Retainer Switch" to close, telling the BCM that the top is being unlatched. The BCM lowers the windows.

The roof is not considered to be open at this time, so if you push the button, it will beep at you.

2) You push the top up and away from the windshield frame. Now, that switch pictured in James' post is allowed to relax, which closes the switch. This is the "top open" switch, and it is in series with the divider switch in the trunk. If the divider is up, and both switches work, they, in series, apply a ground to the TCM's "ROOF/CARGO DIVIDER SENSE" input. Now the top is considered to be open AND the divider is considered to be up! This is important, the ROOF/CARGO DIVIDER indication is an "all or nothing" thing.

If you push the button now, the system will allow the TCM to lock the ELECTRIC lock on the trunk, then start the hydralic pump, activate valves and release the rear bow (the clamp thing that holds the window frame down to the deck lid). This is the beginning of the process of opening the top.

So, if you turn the handle, the windows go down, PERIOD. If they don't, the latch switch is bad.
If they do down, but the system beeps at you and won't run the pump, then:

1) You are going over 9 mph or,
2) The "top open" or "cargo Divider" switch is not closing or,
3) The car's battery voltage is too low to run the pump (not likely if the engine is running) or you have a fuse blown, or you have a bad pump (not likely) or some other odd wiring problem exists.

What wiring problem could it be? Well, there are many connectors in the wiring harness that makes up the top system. Corrosion at a plug/connector has caused ME some problems with fuel system electronics (like when I allowed water to drip down on the connectors on the top of the gas tank and it caused a fuel pressure "too high" indication from the tank.)

James, let me know how it goes!
Others reading this, you can post here or click my username by my avatar and choose the option of sending me a PM.