Home Depot
You can buy 6v photocell dusk to dawn switches from Acetek photocells
The neutral is needed for the internal sensing electronics inside of the photo cell switch.
First check the fuse. See if it's blown and if not check it for 12V with a test light. If you have 12V at the fuse go to the bulbs and be sure they are not blown. If not go to the brake light switch. You should have 12V going into the switch. Depress the brake pedal and check for 12V coming out of the switch. If all this checks out okay the problem would probably be in the signal switch. Do the emergency flashers work?
Yes, there are may online stores that your can buy a 12v rechargeable battery at such as www.nextag.com/12v-rechargeable-battery/products-html along with other stores.
The photocell would typically control a relay. The power to the lamp would go to one pole of the relay and the lamp to the other. The common wire and ground would go directly to the lamp. The relay would be normally open and would close when the light energy on the photocell decreased to an amount that would trigger a circuit to close the relay.
1967 first year for 12 volt
http://www.mgbhive.co.uk/
wherw can i buy a 12v23va adapter
Depends what current out you want. Step-down transformer and a bridge rectifier and smoothing curcuit, or switch mode supply. Spend less than a tenner and buy a battery charger
12v switched source. such as headlight switch or dimmer on the dash.
the roof is slanted so you will need to put your photocell on the side of the roof where the sun is shining