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

Very simple. The key switch only has 3 outputs. ACC is powered in the "ACC" and the "run" positions of the key That line powers stuff like radio, wipers, heater

The "run" position of the key powers things like the gauges, the warning lamps, the ignition system, and the VR and alternator field, and in newer models, smog devices under the hood. THAT "run" power goes DEAD when the key is twisted to start. That means the warning lights go dead during engine cranking

In the start position, there are two separate isolated key switch contacts/ circuits live. 1 is the "start" power which involves the start relay and neutral switch, and energizes the starter solenoid. 2. is the coil "bypass" circuit which feeds full battery power to the coil side of the ballast resistor. If you have electronic ignition instead of breaker points, that power during cranking also BACKFEEDS through the coil ballast to provide power to the ECU for spark.