I read your post three times and STILL couldn't understand what exactly you are talking about.. must be getting tired here!...

Now here are some ideas... since you have the lights turn on and off only when they are at one specific point. why do you use 360 lights to begin with? Lights themselves don't render anyways! Just create one light and have it stable to where the pointer is and have it light on and off as the wheel gets in to the right position.
There are many ways to do this. The fastest would be to write an expression, a less advanced (but more work) would be to keyframe it.

And actually if you have letters or numbers that are on the wheel just like those game shows maybe it is just better you just light it up with incandecency. Have two texture sets asighned to the object. One set for the colour texture and another set for the incandescency. Having the second one be a projection texture that only projects to the specific area that the wheel passes. If you also use an aditive to the shader network you can have only the lighter parts that don't have a sort of text or number on it light up a dear bit more.

If I really misunderstood the whole problem and made it even more confusing I am really sorry. As a result if a wheel spinning around and a segment of it lighting up in only one specific part as it passes this specific point as it spins is what you are talking about: there are really alot of ways to do it.

Hope this helps

Black