A "tacho" (the hour counter inside the rev counter instrument) might measure various things.
Some will measure purely engine running time, but they actually count revs so the "time" will be right only at say 2400rpm.
Some will measure engine running time but only if above 1200rpm or so (I have one of those).
Etc.
These threads always run for ever. There is arguably only one equitable way of doing this: charge for airborne time, and charge for fuel separately.
Technologically this is possible but since there is no tamper-proof flowmeter, you have to take it on trust that somebody has not fiddled with it. I have seen both ordinary renters and instructors fiddle with the flowmeter, to reduce the bill.
In practice almost no flying school is going to install a flowmeter; it's about £2000.
And as has been pointed out, charging for airborne time only results in an hourly rate which appears uncompetitive. You can't win.