How do I trigger capacitive touch screen electronically (without hands)?
You could try something like this :







simulate this circuit &ndash; Schematic created using CircuitLab

The GND should be a return path, allowing the capacitors in the screen to detect a return path, similar to the one created by you touching the screen.
This could not work if the leakage current exceeds the detection threshold of the capacitive screen, but it's worth a shot.