You'll need a DC-DC converter that can output the current your headlight requires, at minimum, that takes it's output from your main battery's output. If you use the headlight all the time, just wire the DC-DC input side to the battery on the controller side of the main battery power switch (if you have one). If you prefer a switch, then you can get handlebar-mounted (or wherever you want) switches to control the input to the DC-DC from the main battery. Just get one that is not "momentary" (or else you have to hold it down to keep the light on).
IF you prefer to use the existing headlight function, and there's no documentation for it, you'll have to testing to determine both how to use it and how to wire it.
For the UKC1 button, which wire that comes out of it or it's wiring harness changes state when you use the button to change state of the headlight function? THat's the wire that you will use to control the DC-DC that powers the headlight. How that control will work depends on how the UKC1 control wire works.
Set your voltmeter set to 200VDC. Black lead to battery negative. Red lead to first unused wire coming out of the UKC1's wiring harness. Power system on. OPerate the headlight button. If teh wire being monitored didn't change voltage even a tiny bit, it's probably not the right one (depends on how it works). Red lead to next unused wire. Operate headlight button. Etc.
When you find one that changes voltage only when the headlight button is operated, that's the one the button is controlling. If it changes from around 0v to some higher voltage (probably either 5v or the battery voltage), then this can be used to drive a relay to switch the DC-DC on. It is probably a very low-current signal, so directly driving a DC-DC or headlight from it may damage it.
Once we know what signal it makes, we can figure out a control method using it.