Ahh, I get it. Hadn't seen those before.
Yeah, those lights use a custom plug, but to my untrained eye, it looks like the standard red-white-green-black, plus a couple extra wires added on (maybe those control it? I don't know; just guessing).
If I had to guess, I'd say that it's probably possible to wire it yourself among those first four wires to make it shine continuously. Although I admit that figuring out exactly HOW you'd wire it is not my strong suit and you'll probably want the opinion of someone better versed in that kind of thing.