Is it possible to script a light source, such as a Dwemer bulb, to be able to dim when the player interacts with it?

Most likely, it can be possible if using the right scripts.

Technically, no, but for all intends and purposes, yes.
You just have to create two lights, one bright and one dim, your script will then have to enable and disable the two lights based on that "interaction".

I once made house lights from terrific crystal balls made by... a talented person whose name I can't recall just now. Anyway, I had a wall activator that counted in three stages, so if I activated it once, the lights were bright, twice,they were dimmed, and the third position was off. I did that by enabling and disabling three different lights, as was previously suggested.

In the http://planetelderscrolls.gamespy.com/View.php?view=Mods.Detail&id=9163 housemod there are lights with 3 stages. http://grotto.moddersrealm.com/index.php?action=downloads;sa=view;down=40 also had a working light in the bedroom. You'll have to register to her site but it's well worth it IMHO.

Use duplicate lights? Hmm... Simple enough I suppose, though now I'm thinking that the particular area I want to apply this trick to could do better with pick-up lights instead of wall-mounted ones.