The led flashlights all have fingernail sized SMD boards like these, I ruined more than a few with the iron! 20mm is cake after the stupid 14mm in AA flashlights and if it hadn't been a simple fix I'd have tried a whole board swap.
I have some 2 mode Hi/Lo boards, though they'd need some reduction of current.
PWM is a high speed switch with variable ON/OFF ratios that the eye sees as reduced brightness, the load sees as reduced voltage.
Of course on the dim settings it's mostly off and that makes the PWM efficient and versatile, and solid state
Some drivers incorporate a 3 leg voltage regulator (like LM78xx), using led VF to control current. Multiples can be paralleled on the board for increased current.
There are also constant current drivers.... but I don't actually know how they work.
Led are very sensitive to voltage changes, the characteristic VF defines this sensitivity, with the entire current handling range sometimes occurring within +/- 0.2vdc
VF varies somewhat even throughout the same binning, so there are no absolutes, but it has been my impression that newer led have lower VF and they are still getting lower.
One Cree I set up on voltage variable driver behaved like firstname.lastname@example.org email@example.com
An older bin wouldn't even turn on @3.2vdc was closer to firstname.lastname@example.org.
Of course that is a completely different class of led, just offering examples.
Crap, now I want to take apart the 1-11 unit....I wouldn't put it past them to have wipers on a resistor like some $0.18 pot....