Christmas LED dimming circuit with potentiometer
Going out on a limb here because I don't have experience with these constant current contraptions, so please let me know if this is hare-brained or not:
The supply is rated at 3.6W, 31V, 116mA.
So it seems likely the circuit is a bunch of parallel LED strips each running drawing 5mA or whatever.

So why couldn’t you just put a variable resistor across it to siphon off some of the current?

True, some drain occurs even at max setting. Make the 470 smaller if not bright enough.