Smart(?) switch.

When I first got my cheap headlamp it took four pushes to go from on to off.
1. 2 LEDs
2. 3 Leds
3. Incan only.
4. Off

After a few weeks it only took three.
1. 2 LEDs
2. 3 Leds
3. Off

I thought it was broken but the "missing" position was interesting. I thought it should have been.
1. 2 LEDs
2. 3 Leds
3. (nothing)
4. Off

Last night nothing happened when I turned it on and after replacing the batteries the Incan comes back on.

I'm guessing it's smart enough to "know" when there is only enough power for the LEDs and my batteries were old when the unit was new.

I have several headlamps that have
1. 1 red LED
2. 2 white LEDs
3. incan
4. off

when the batteries get low the incan doesn't have enough power to light
but the LEDs can still light up. The light has no smarts it is just incans cannot
even light up at all when current gets low. Most incan bulbs are 200ma+
while LEDs can light up at 5ma easily. So most likely you only have enough power to light up a 50-100ma incan which wasn't in the light.

That's fine but do you have *two* positions where the light is off?
One where the incan does not light and one where the light is off?
I don't.

Mine have two off positions, that is somewhat odd. Have you tried removing the incan bulb with fresh batteries to see if it skips the incan.