12 Volt vacuum pump problem

Shouldnt matter with engine running or not. Checking amperage draw with engine running will give you some idea.
Vibration causing something internal in pump to short?
My choice? Circuit breaker 15 amps. Bet it draws near 10 amps, perhaps more. Not many auto electric motors draw less than 10 amps.

Well yes, it will. Depending on motor design, there's a fair difference between a fully charged battery at 12.6 and "running" charging voltage at 14V nominal.

Let's say you have a 1 ohm load, at 12V that's 12A draw. At 14V that's 14A draw!!