When the pax (read lessor) decides who will be the pilot, and where & when the flight will go - they have operational control. If any other body has control over any one of these then the pax does not have ops. control and the flight would not be considered a legitimate lease, operating under Pt 91. Now you enter the dubious world of '134 1/2'. Be prepared for a profoundly unpleasant time if the FAA catches you.
Part 91 doesn't have flight & duty time limits, apart from careless & reckless ops. If the op is part 135 (as most 135s operate) then *all* rest must be proscriptive. *No* rest can be retroactive. Doesn't matter if it was daily, weekly, monthly, or quarterly. If you can't plan to have a beer, then it does not count as rest. No amount of 'well, we didn't call you so therefore it's the same as rest', or 'we won't call you but be ready to answer the phone' passes muster. There are numerous - and consistent - FAA legal interpretations of this going back 20 years or more. It is not open to interpretation.
Something else to consider: Under Pt 135 many have maintained 'legal to start = legal to finish'. Not quite so. WRT to *flight time* that can be the case. The regs. specify extensions to flight time limits, and the rest penalties as a result. BUT! They do NOT specify any normal way to extend duty time ie unless it's an emergency - which allows you to break any rule to deal with that event for a safe outcome - you cannot extend *duty time*.