There is a type of clock that is powered by pressure difference from day and night air differences. You likely could adapt it so the thermal expansion battery/generator chamber is filled with gasoline instead of air. >>11117955
this, although I offered the best idea I got above
There is a model for gate switching in transistor and stuff out there that measures the energy of the disorder in glass. I'm sure you could use those to very accurately define how much energy is needed to tell time. As they tell how much energy is needed to move atoms to there alternative locations, and can include a kinetic component. So you would be calculating how much energy it takes to move the atoms to change the declared state of the clock, and over what time that would happen.
energy to move atoms to new state in clock in 1 second / 1 second of time = energy need for the clock to tell you time
A mechanical clock you could do something similar. But could use mass of hands and loss to motor a gears instead of charged atoms movements to avoid quantum effects.