I suggest clearing all codes for the soft top. Then perform a raising or lowering operation and once it fails retrieve the stored code. Complete the operation manually and clear the codes again. Now do the inverse operation (you indicate problems with both lowering and raising) and once if fails retrieve that code too. You access the codes at Pin 10 of the diagnostic connector. The procedure is explained several places on this website. Once you have the codes I can interpret them for you.

You state that when lowering the top the compartment cover opens and then motion stops. The controller may not recognize the cover is open or there may be another problem. You can plainly see the limit switch that detects the cover is open. At any rate, the diagnostic codes should pinpoint the problem.