Dash Oil and Brake Warning light - how are they triggered in the start function?

I don’t have the time to open a schematic to show you that the warning light for brake and oil is powered at the instrument cluster all the time, and when the brake or oil light switch itself gets grounded it completes the circuit which illuminates the light.

It’s in ALL the SERVICE manuals. Look it up yourself.
No it is NOT powered "all the time"
It is powered ONLY in RUN by the IGN1 circuit. It is backfed BACKWARDS through the ballast resistor by the IGN2 circuit during cranking BUT the ballast is loaded by whatever else is on that line.

YOU look it up. If you CAN NOT AND WILL NOT prove your point then don't come here and argue.