Making assumptions on how circuits work also wastes lot of time on troubleshooting as well. Injecting external power into circuits is artificial and doesn't tell you anything about how those circuits work or are not working. Can also damage sensitive components in ECU. You'll want test by
measuring and coming up with
numbers at various parts of circuit to determine functionality.
By looking at wiring-diagram, we see that power from ignition-switch does not go to headlights. It goes to headlight-relay which is open/off. To determine what it takes to turn on headlight-relay, measure all junctions between battery and headlight-bulb:
1. measure voltage coming out of battery
2. measure voltage going into ignition-switch
3. measure voltage going out of ignition-switch with key ON (yours may be broken)
4. remove headlight-fuse and measure resistance between legs (if I had nickel every time fuse "looks ok")
5. measure voltage going into headlight-relay (this may be broken too)
6. measure resistance between ground of bulb-socket and chassis-ground
7. measure voltage going out of headlight-relay to bulb, then crank engine.
Then it'll all make sense. You can't force circuit to work other than intended (other than re-wiring it). Measuring actual voltage allows you test wiring in between junctions as well. If you see voltage dropping unnecessarily between two junctions, there may be broken/corroded wiring or bad connectors.
In this case, headlight-relay is turned on by stator-coils getting enough power from engine spinning (goes through diode to convert to DC to activate relay). Once relay is activated, its output-power going to headlights is looped back to its activation-coil to keep it on. So once it's on, engine-cranking is no longer needed to keep it activated. As others mentioned, headlight will stay on after engine stops spinning.