Need a little help applying this lesson to my current situation (Holley Terminator X)

The installation instructions state that the main power harness on the Terminator X must be connected directly to the battery, and that it should not be switched, so I don't think it should be on a relay or going through a killswitch. Please correct if wrong. If I connect it directly to the battery, but have all other power going through a killswitch or high-amp shutdown relay, and am sure to actuate those before disconnecting battery connections, will I avoid any possible backfeeding? Please feel free to ask questions.

Eric,

You'll want the kill switch to be able to kill ECU power for most rulesets and for safety.

I haven't wired that ECU, but it sounds like they're wanting a power source which is present without "ignition switched" power being on. This is typically to allow the ECU to shut down gracefully when ignition switch is turned off so it can stall the engine, save a log that may be in progress, wrap up any processes, and then when you kill power it shuts all the way off.

As Mike said, other options that may apply are priming the engine, logging, running cooler fans post running, etc.

Think of it as being like your PC/laptop/'phone - while you could turn them completely off, by leaving them powered in 'sleep', or similar, mode they can do background checks, etc, that would otherwise be needed to be done on start-up.