Wait. How do those #44 sockets work?
I'm ?every? application I've seen on older Solid state games... there is a diode to one lug... and a ground stapled to the bracket.
I'm betting if you ohm out that lamp socket; you'll find you need "negative" on the mounting bracket... and "positive" on the "center" tap.
The way you have it wired in that picture means one of your power supply leads is going to nothing / IE not connected to the lamp. IE I think the non-centertap lug is insulated (with Bakelite) from both the center and bracket.
PLEASE verify why I said above with a dvm… I'm have NOT checked in a real game. I may be remembering incorrectly.