If that's a 9 light strip, there's a few out on Ebay - why not just replace the whole strip?

ebay.com link: HYPERBALL 81 WILLIAMS PINBALL MACHINE PLAYFIELD 5TH BOTTOM 9 LIGHT SOCKET STRIP

ebay.com link: HYPERBALL 81 WILLIAMS PINBALL MACHINE PLAYFIELD 6TH BOTTOM 9 LIGHT SOCKET STRIP

what you guys spend on wine we spend on pins instead

Are these lamp strips pretty well standard in WMS games? I could probably make a FR4 PCB strips with the quarter turn 555 lamp twist in holes pretty darn easy and cheap.

Pop rivet the old socket into place. Alternate, solder wires directly to the LED/bulb and cable tie it into position using 3-4 ties.

Not sure how standard the spacing and count is, but a lot of williams games have them, even back to some of the EMs (Grand Prix has four separate 10 lamp strips...)

I had a friend make me a lamp clincher jig.
I was able to fix a handful of Bally and Gottlieb lamp sockets.

Got a picture? That would be cool to see.

Basically, it is a round base with a hole in the middle with a recessed groove
that fits the round lip of the eyelet. The striker is a round cylinder that fits
into the lamp socket and it to also has a round tongue that fits through the eyelet
and into the hole in the base.When you strike the clincher it slightly flairs the inside
edge/lip of the eyelet inside the lamp socket.

It's kind of a cinched cylinder with a long rivet inside of it.

You might be able to solder the base to the strip, then set the long rivet with the spring.

I know what you can do. Cheaply, and not too hard: Buy a new replacement socket with the same length on the barrel/socket. Use a Dremel Tool and a cutting bit to enlarge the open hole on your bracket. Take your new replacement socket and bend the strap/tang back so you can insert your new socket into your now enlarged hole. Cut of any excess of strap from socket and solder what is left to your bracket.

Your new socket will only be setting lower by the thickness of the bracket which will not affect how the lamp displays.

Short answer: Open up the hole in your bracket and solder a new socket in from the backside.

Depends on what you solder with. Electrical soldering does not make a reliable mechanical connection. Even when soldering a simple stranded wire this requires wrapping the wire around the terminal or lead through hole and wrapping before soldering. Using electrical soldering for this kind of repair is questionable.

Good point. It is hard to say from the picture but it looks like the bracket might be big enough to drill a small hole and attach the socket material with a small machine screw and bolt. Or for that matter, one could drill out the brass "ring" that is attaching the mounting bracket to the main bracket and screw the socket bracket to the main bracket with that machine screw and then sweat some solder on.