You are logging the hours as PILOT in command not autopilot in command
Maybe the autopilot or George should have its own log book and be programmed to keep it
Fact is there are many automated systems or pilot aids which make up a modern aircraft and the Pilot in command is in charge of operating and flying the aircraft which will also include constant monitoring of the systems autopilot included. ready to take over at will if anything is not doing its job properly!
I have flown a number of older Citations and a few have had suspect autopilot behaviour, pitching on altitude capture etc.
workarounds include disconnecting manually levelling and reconnecting to stop the PAX having a boat ride as the aircraft pitched up and down.
So as in life trust nothing including the autopilot. The danger is relying on these systems for lack of piloting skills and more and more accidents are due to lack of piloting skills and reliance on pilot aids to cover up those lack of skills.
so all these systems autopilot included should be there to take the work load off pilots not to substitute for poor pilots flying out of their ability zones
Pace