Couple of months ago, I saw a Prius at 10pm Sunday, apparently going home. They ignored my hints that their headlights wee off.

I considered that the headlights may have been off on purpose. Maybe they were almost home and wanted to be in the electric-only mode. Sound plausible?

 

Nope. The headlights won't turn the engine on. I have no idea how much power they actually consume (or even which battery it's from), but in my year and a half of driving I can tell you it's got nothing to do with it

 

Headlights draw ~55W each, and the power comes from the 12v system that is fed by the HV battery through the 100A DC-DC converter. Usually the Prius won't turn on the ICE to charge the main battery unless it's very low, or it needs the heat (or A/C) for the cabin. The HID lights use ~35W each, so there is a real advantage to having them, other than the brighter, whiter light.

Now, if you run out of gas, then it would make a lot of sense to turn off the headlights to save power since it all comes from the same place. Maybe they thought that it would prevent the ICE from coming on, but I don't think it would have affected it.