Interesting how much - variation - there must be in operating habits, and assumptions.
When I rented here in the US, all flights were timed (for rental cost and logbooks) from the Hobbs meter.
I assumed (was told) the Hobbs ran on engine time, since it was used for determining time to next overhaul. But it didn't really matter. The difference between Master switch time and engine time amounted to seconds at most.
Hop in - master ON - lower flaps, check fuel gauges as flaps came down - master OFF. 20 seconds at most. Add one minute if you had to radio-call fuel truck for top-up. Do walk around with power off.
External checks and most internal checks done without need for electric or engine power. Master switch was turned on again just (10 seconds max) before starting. Never ran avionics off the battery alone - I wanted that juice for starting, plus didn't want the AV on during start in case of voltage transients. Logged Hobbs reading just before engine start.
Rentals were all "wet" - fuel included in hourly price. Once I started the engine, I was burning the owners' or club's fuel, and eating into the time before next overhaul. Perfectly reasonable I should pay for those, even sitting still. Or taxiing.
On arrival, engine shutdown and master switch OFF were virtually simultaneous. Click-click, click-click, click-click. Logged Hobbs time.
On general principle - if you are tying up a rental/club aircraft that could be rented to/used by someone else, you pay for the time it is not available to other customers. Doesn't matter if you just go out and sit in a cold cockpit for an hour - that's an hour it could have been earning revenue from someone else. Dog-in-the-manger principle. If I flew an overnight, I had to pay a "day-minimum" equivalent to 4 hours engine/fuel time, per day the aircraft was not available to others - careful trip planning meant I always flew at least 4 hours per day average over the trip, so it never actually applied.
The fact one is only charged for the running time is itself a good deal.