'fraid that a little bit of effort producing the circuit diagram from the boards is really needed.
I think that it will show what has to be a microcontroller with an input pad going to the switch and another pad going to a base resistor for q1. Q1 switching power to LEDS via RA - D.
The long light looks to be fitted for a an IR receiver. With U1 near it possibly the decoder. As they show the thing stuck on a rafter presumably way out of reach - I suspect that 's a picture from the version with an IR controller. They have produced a cheaper version, without the sensor and re-used the photos.
Now, if that’s how it is - I’d just remove the microcontroller and glue one of my favs upside down on the board and run wires from its pins to the relevant pads (removing the existing microcontroller). I haven’t bought one recently, but 8 pin ones were costing me less than 50p… Having programmed the replacement with an added option to stay on.