Some hour meters are wired to the switch directly, and some are wired via an oil-pressure switch so they only run when the engine is running.

Sounds like yours may be wired directly to the switch........leave the key on and the meter will run.
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She was standin' alone over by the juke box, like she'd something to sell.
I said "baby, what's the goin' price?" She told me to go to hell.

Bon Scott - Shot Down in Flames