Engine tachometer - How does it work?

I’m in a club that charges by tach hour and I’m wondering if there is an ‘optimization’ for flight to minimize the cost of a flight.

I’m understanding that in cruise setting the tach runs at clock rate, above cruise it runs faster than clock and less than cruise it is slower than clock.

Does anyone know exactly how this works out? Is it a linear device that just counts RPM so XX rotations = 0.1hrs? Or are there ‘stages’ where it runs at several different fixed rates? I can’t seem to find this info anywhere.

I cant recall completely but I have owned airplanes for about 24 yrs and I think above a RPM (1200-1500?) it just counts Hrs. Doesn’t matter if you are at 50% or 80% power it logs the hours. It is using that number to track engine maintenance. If your club is charging Tach you are way ahead of getting charged Hobbs. Hobbs is how flying schools make a profit!

Tach hour meter uses a preset rpm, say 2400 rpm, as a reference point and counts “time” relative to that rpm.
Running the engine at a higher or lower rpm will make the tach hour meter run faster or slower.

In exaggerated terms, running the engine at 3600 rpm for 1 hour would result in 1.5 tach hours, whereas
running 1200 rpm would result in .5 tach hours.