In the past, I have used an electronic relay off the low oil pressure alarm circuit to supply power to a 12V fan. Electronic relay, because it had a 2 mA draw. If the fan had been put across the circuit directly:
1. the oil alarm would always be activated because the fan would act as a ground.
2. the fan would not run because the alarm has too much resistance.
I know, "Big Deal" so much for my case. But here's my point: check out the amperage draw on your electronic hour meter when placed across your 12V battery using a multimeter. If it's only a few mA, you should be able to pull power from your oil pressure circuit without sounding the "low oil pressure" alarm.
I know you know this, but I'll mention it anyway: tap into the oil pressure circuit AHEAD of the pressure switch or you'll be on the ground side.
I can't find any info on the power required for an electronic hour meter. Let us know.