How to physically stimulate a touch screen with an external device
I'd suggest that you will have too much capacitance in the FET to give reliable results.

When the FET (and I'd use P-Chan in your circuit) is off there is typically hundreds of pF of output capacitance.

I'd use a Reed Relay where the open circuit capacitance is extremely low, just a couple of a pF maximum. This gives you the maximum possible change in capacitance to be recognized by your touch matrix.
I'd also use round capacitor targets rather than square.







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