I built a servo tester with a 555 timer, years ago. Got the circuit off the web, should be an easy find with Google, also posted on here several times. I'm using microcontrollers for such things now, that was one of my last 555 projects. Anyway, it uses a pot to move the servo arm, so you just need to determine the value of two resistors to replace the pot, and the toggle switch to choose between them. An LM7805 should be fine to drop the 12v down, but will need a heatsink.
Personally, I would mess with the tag, law enforcement around here are a little particular about them. They pull you over if its bent, muddy, not mounted in the correct place, or pretty much anything. It's very tough to spot them anymore, they'll drive any model car, some marked, some not, the light bars are all low profile LEDs anymore. You get caught, you will most likely go to jail, or be detain quite a while, until the decide what to do. Most cop cars have dash cams these days, to limit liability. IRLEDS stand out very well. Should probably think about this a little more, decide if it's really worth it. They don't like altered tags, specially when it's intentional, since the assume you have some crime in mind.
Don't know how big your camera is, but I have some that are pretty small, and a tiny hole through a taillight would only be needed. Shouldn't be noticeable, and a dozen or so IRLEDs could be placed anywhere, also with little work, or alteration of appearance.