It's pretty common for the pins on those lamp boards to develop cracks in the solder joints. I'd reflow the solder on the lamp board pins.

When you wiggle the connector, your ensure a good contact. When you let go, the contact is broken, so i suggest you pull the connector and inspect each contact. Ensure they are clean and serviceable (not loose). Reseat the connector (firmly) and try again. Otherwise you have a loose/broken wire somewhere near the connector.

bad solder joints can also be a problem.

You could have a broken trace on the lamp board or, a bad diode. Do you know how to test them with a meter? Did you try to swap working sockets in to confirm the socket is ok? Push the wires back in in the hardness that connects to the little lamp PCB? If that gets you nowhere, trace the wire that lights that insert lamp to it's previous lamp in the matrix. A wire could have come loose (or been sliced through) from the previous lamp connection in the matrix. After that, you are looking to board issues.

Looking at the manual, all the GREED lamps are in column 3. Since the other lamps on the board are lighting properly, you know the column 3 wire (the yellow one) is fine. Also from the manual, the 'R' is in row 2, and is controlled by the red/black wire.

The quick test is to put your DMM on DC voltage, then put the red lead on the yellow wire and the black lead on the red/black wire. If you see voltage (when the lamp should be lit), it means the red/black wire is fine up to the point you're probing and the problem is on the lamp board. If you see zero volts, there is a problem with the red/black wire before it makes it to the point where you're probing.

Wow, that's way harder to put into words than just showing someone in person!

Check the header pins on the PCB where the wire harness connects. The solder may have cracked.

I agree!

We've been over that four posts up.

If you're reflowed the pins, and a lamp still doesn't work, it can really only be two things (presuming you have ruled out a broken wire elsewhere under the playfield) ...

1) the diode is bad for that lamp
2) the solder on the twist-lock pads is "dimpled" and the twist lock isn't making contact when it's fully turned and seated.

You can easily check #1 with a meter ...#2, just heat the pad, tilt the PCB slightly so the solder pools in a slight uphill slope, and let cool. Repeat for other side.