These lights are from Deals Direct. They have 8 channels; 1 for each ring of LEDs.
The controller has no button, hence they just do their own thing. The power supply is 24Vac 200mA. Diameter is approx 800mm.
Each ring contains 20 LEDs and appears to be split into two parallel strings of 10 LEDs, so 40mA per channel will be the target current limit.
I added a 150 Ohm 0.6W resistor in series with each of the RED channel wires only. These values gave me 20mA – 40mA current draw per channel (varies with LED colour) from 31V DC.
Here’s a video of it in action with the original controller and power supply.