The simplest experiment would be to simply have a gadget with a bottom and top electrode and generate a high frequency high voltage oscillating voltage between them
So obviously a capacitor ... because that's what two parallel electrodes are. When I say high I mean 100s of volt BTW.
A magnetic field will do bugger all to a touch screen. What the digitizer is doing is putting an excitation waveform on a column wire and seeing how much displacement current it causes on a row wire, when your finger is near it that changes. What the gadget I describe would be doing is forcing its own displacement current into the wires, at it's own frequency, in the hope of causing the device to sense an object. Which might work, or might completely screw up its automatic calibration algorithms.
Sensing the excitation itself and amplifying the effects to correct for the much lower parasitic capacitance of the gadget relative to the human body might be possible too, but would make for a significantly more sophisticated circuit.
PS. this is not an easy problem, which is why no one has solved it yet. The fiducials which just detect the patterned electrode on the bottom while you are touching might not exactly meet your requirements, but they are a lot easier to
make.