To determine the exact nature of the clog, to allow more optimal unclogging, I
propose to use sonar.
This could be integrated into the toilet, or an add-on device (or even a portable
device, which would be more cost-effective for janitors).
It uses either transducers coupled to the porcelain
of the toilet to transmit sonar
pulses into the toilet and detect the reflections, similar to how frustrated total
internal reflection touchscreens work with light, or a transducer that you stick into
the water/soggy toilet paper. The return signals are processed using DSP, and the
shape of the clog is displayed on a screen.
This provides feedback to the unclogger, so it/they can optimize the unclogging
technique for the characteristics of the individual clog.