This might help you understand whats going on, i've taken your pic from your first post and modified it slightly 
The 2nd lug, its whole purpose in life is a tie point for a diode on games that have a lamp matrix type setup, so it has NO connection at all to the barrel portion where the lamp fits in, hence why your lamps dont work! Notice in the pic i have indicated on the drawing of the socket(s) where the wires would go.. notice the green/red lug goes directly to the barrel portion whereas yours is insulated.
You would really have to solder the green/red wire to the barrel as i have indicated in the pic below.. this would work BUT.. as pointed out by ballywannabe it might need to be insulated from the coin door where it screws on.
that's exactly what I figured but wanted to check. Thank you wry much for the confirmation
