How can I turn on a switch with a small and short voltage that will in turn turn on the device?
Any electronic switching circuit would work for your application.
So, here is what needs to be done, search out and get as much information on piezo, sensors, (google), then purchase if applicable one of each that could be a likely candidate for this application.
Then test each one and gather huge amounts of data, by placing them under changing pressures, simulating the greatest pressure they would be succomed to, then testing for leakage signals, as well as how they cooperate when the pressure changes, such as coming closer to the surface, there will be a changing output there too, that you must record.
Once all this is established then you can bring to the table this data, voltages and currents under different pressure situations, greatest amount of voltage change, and any residual voltage signal leakages while under a constant pressure, mark out the amount of voltage change that occurs incrementally at different pressure changes, so as to find the peak voltage, current output under the 0 pressure (when it is surfaced).
Then when you bring all that data to the board, there will be a logical way of implementing this device to operate as desired.
As of right now there is no electronic parameters to work in, so everyone is just guessing at how it could work, with no concrete analysis of what to do to make it work.
So you have a lot of research and development of testing these sensors, to where you know exactly what voltage , current, thresholds need to be met.
That a electronic switch can be activated with.