Theoretically, it doesn't matter which wire goes to which lug on an AC GI Socket.

HOWEVER, most EM playfields are wired with those "rail road tracks" of bare braid and one of them is common and MAY also be used to connect a playfield switch, and/or a feature lamp socket (Also AC). And in both case, it DOES matter which common wire is looped from item to item. This sharing of wiring will not be shown on the schematic (other than in the same colored wire) but may become obvious if you track the bare wiring all around the playfield.

If you are replacing the sockets, either re-use the existing track wires or replace both runs of wire and duplicate the route on the playfield (mark it in pencil before pulling them up).

In AC vs DC. There may not be polarity in AC, but there is still a hot and a common just like in DC.

Related question: If I have an entire set of of GI that is out (under one piece of plastic), does that mean that one of the sockets has come out and is making the rest inoperable, or is it likely something else?

Some of the sockets are old. And rusted. And nasty. If there is a short in one, would it knock the rest in the group out?

Typically, an EM had a single fuse for the 6.3VAC going to the playfield. And often a second 6.3VAC fuse going to the back box/head. On the playfield, that would/could include both GI and Feature lamps. So, it would not normally be possible for a section to be out unless it was a broken wire that chained around from socket to socket. And then you would lose every lamp down stream of the break. If there were 1 bad, shorted socket, it would take out the fuse of all the others. And no, one socket should not effect the others to not light. They are not in series like mini-christmas tree lights. They are instead, like the larger bulbs you used to use on your house - all in parallel. If one goes out, the rest stay lit - Again, unless its a short and blows a fuse and then they all go out.

Early SS games may have had at least 2 circuits feeding the playfield GI lamps. So, it would be possible to lose approximately half if you had one burnt pin. On later SS games, the 20 AMP Fast blow fuse just couldn't handle the heat so the circuits were broken up into four 5 amp circuits. And on WPC games, you have 4 Triacs controlling the 4 branches along with a fuse for each.

Sockets are not always the problem. I have had bad new bulbs (shorted), where once installed, started blowing the GI fuse. Its a bitch to go back and find the bad one if you just replaced every single GI bulb with new ones. So, it helpful to replace them with the power on.

Thanks for the informative response!

No, there are wire in parallel, if one is broken the others will still work. You have a power getting to that cluster issue.