Yeah you'll be cutting off the switch that came with it. You'll have to look for the documentation for the neon's wiring. My omniscience has its limits.
If you had a multimeter I would suggest hooking the neons up to your battery and identify the wires. Harbor Freight has a coupon for a free multimeter with any purchase. I bought a $1 item to get an extra multimeter just for the hell of it. Or you could go to Sears and get the same $15 multimeter that I used for years as a pro installer.
Dimmers don't work on everything. If you wanted to try it you could replace the override switch with a dimmer.
The whole thing could be done in 30 mins on your first try. 5 hours is enough time to gather all the supplies, get drunk, sober up, take the wife and kid to a movie, come back and do the install. Sounds like my typical Saturday.