The little pink single-wire connectors are called "quick disconnects" or "QDs". There appear to be 8 of them. 4 were likely connected to the lamps (2 to each lamp). The other 4 were likely connected to either the microswitches under the coin mech, or to "lockout coils" which prevented the mech from accepting a coin when power was off (or whenever the PCB didn't want to accept a coin).
There's also a 2-position Molex connector which appeared to connect to something on the coin door--not sure what it might have been.
On the other end appears to be a matrix (grid) style Molex connector. I can't really tell from the pic, but I'm guessing it's either a 6-position or 9-position 0.093" connector.
You could re-install that harness on the coin door, re-connect the QDs up to the lamps, and trace the proper wires back to the Molex connector. To mate with it, you'd need to get some wire, crimp on the proper pin terminals using a crimping tool (not the common type of crimping tool used to crimp on QDs), and insert the terminated wires into the proper mating Molex housing (to mate with the lines you traced from the lamps). On the other end, you'd splice into whatever type of connector mates with your PS, at the proper voltage for whatever bulbs are in the sockets.
Or you could leave that harness out of it, and make you own wiring from the PS to the lamps.