You may have considered this already… if I understand what you're trying to do:

The Aux switch input on the TimeFactor must be a stereo cable otherwise a mono cable will be constantly reporting that the "ring" switch is being activated.

If this is even an issue, a get by solution is to partially insert the 1/4" mono plug so that the tip is making contact with the "ring" connection inside the jack. Set the TimeFactor to receive tap info on the "ring" and insert the the other end into the ground control.

This way whenever the relay latches in time only the "ring" will be grounded.