So this is up my alley. I rehab bikes, boats and cars. If it were me, I'd hide a 12v charger and power the battery. Then fix it up and I'd ride the thing. If it's so old there's no battery I'd add one and a rectifier. I'd still display it inside but be able to take it out and ride it sometime too. Just drain the carb before taking it indoors. When it's hooked up to the charger you can turn the lights on like normal when it's on display.

You can wire a dimmer inline if you insist but I'd try it the way it is now and see if you when wanna dim it.