I really don't understand how hard it must be to look at your watch at taxi start and taxi completion and log that time (provided you intended to get airborne). As I said earlier VDO/HOBBES is the closest approximation to it however it will be erroneous if the recording starts with battery power or extended engine operation prior to taxi.
Maintenance will run off whatever the approved maintenance system specifies, whether it uses tacho, airswitch, cycles, dates, that's all specified in the maintenance manual, not pilot related stuff. Those meters may or may not be reliably recording flight time as per the regulations, most likely they will under-read the required flight time definition for pilots log books. A flying club/org could charge by any switch, dry or wet, day rates, weekend rates, air services in or out, bulk hour rates, or no charge at all, that's up to them. What a pilot logs for legal purposes has been covered, chock to chock for the intention of flight. If the craft taxis by itself, or becomes airborne in a gust of wind, extreme vibrations, earthquakes or floats down the river in a once in a 100 year flood (that's happening every 5 years) etc etc, that is not moving with intention of flight. I once jumped in a self taxiing twin whilst it was moseying along by itself in a strong wind. I did not log the time from when I hopped in and brought it to a stop, as I was not sure that the aircraft had the intention of becoming airborne.
Logging of flight times for pilots has a legal definition, so follow that as per above posts containing the references, especially if you intend to use the hours for qualifications or duty limitations. I've seen passengers keep logs of flight time, there is no legality that says you can't you can log anything you want as long as you don't use it for something you are not legally entitled to.