HEI 1 Wire/Stock Ballast Wires

What year, make and model of A-Body, if you would please?

Connect all of the ballast wires together. The brown will be +12v when the key is in START and one of the blues will be +12v when the key is in RUN. The other wires go other subsystems like the original regulator that need +12v when running.

If you go with a relay switched ignition, then you need to use feeds from both the brown wire and the blue +12v feed wire above so that you will have power to the distributor in both START and RUN positions of the key. 10 ga for that seems a bit ridiculous for just the distributor; 16 ga should do fine for just the ignition. But if you are feeding other accessories from that relay, then perhaps 10 or 12 ga is best.