And both strips have both UV and IR leds, so I would need a controller that can separate them.
Hmmm. This one is another example why I need to keep the pie hole shut until I have all the info.
Now that, I think, I have seen the hardware enough to suspect what it up, I'll dive in again.
First up, I am pretty sure that the black brick is a standard led power supply, presumably a constant current one given that you can turn off some of the leds without screwing it up. The dual switch allows the positive of each led type to be cut off or turned on as needed. The three wires going to each strip are, I suspect, the switched positive wire to the UV, a switched positive wire going to the IR, and a negative/common from the LED strip back to the controller, and the wire to the splitter is three wires, UV+. IR+ and Neg/common. All the spitter does is connect both strips to the single supply/switch combo.
IF,
IIF, that is the setup, you could wire two timers into this setup to control uv and ir separately. This would be best done by cutting the two positive wires to UV and IR
before the splitter, and using the timers to control when the specific leds would turn on. By putting the timers in ahead of the splitter you avoid needing four of them. You would not need the dual switch if you put in two timers because each led bank could be controlled by its own timer, so you could cut the switch out and wire in timers at the switch location.
I am not sure whether there is any better way to do the job. Two power supplies will not do the deed, at least not simply, because you still have to separate the uv and ir feeds to each strip, and there is no way of doing that without cutting wires, at least not as far as I can see. You could just run UV on one and IR on the other with a timer for each one, but I think you would need to do some cutting and joining to be able to use UV simultaneously on both strips.
Quiz MH on what might work, and see if they can confirm that the three wires coming out of the power supply are indeed positives to IR and UV, plus a negative common. It is possible that there is no easier way to do this than what I describe here, but maybe MH has suggestions.
There are at least a couple led light builders on here, but I can't recall who they are, maybe they have other suggestions.
Good luck with it, tag me if I can add more amusement.