Congrats on your new game, welcome to the hobby!
This is a perfect opportunity to learn how your game works and maybe even learn a bit about reading the schematics and manual. I'll try to keep it as simple as possible. A copy of the manual and schematics can be downloaded for free from ipdb.org. Here's the link to your game, just scroll down to "Documentation" and download them (note the manual and schematics are 2 separate files, grab both of them):
Looking at the pic you provided, it looks like that's a brown/white wire. Consulting the switch matrix diagram in the schematics (9th page, labeled "Playfield" at bottom of page), you can see the brown/white wire is at location A4J2-2 (see the arrow at the bottom). That wire runs between all 8 of the switches on the second vertical column in the below diagram (right and left return lanes, Loop, bottom outlanes, etc). I've added additional markings to reinforce a particular point, which I'll address in a moment:
First, the arrow at the bottom--that's pointing to the color code: Brown/white. Now if you follow that line to the left, it terminates at A4J2-2. What that really means: A4 is the MPU board--looking inside the backbox, it's the board at the upper-left. J2 is the name of the plug on the MPU, you'll see it on the right side--it's the upper connector of the 2 on the right side. The "-2" is referring to pin 2 of the aforementioned connector. So, one end of that brown/white wire is coming from the mpu board at pin 2 of connector J2.
Back to the diagram, if we follow that line to the right and up, it intersects with several other lines, and the filled-in circles/dots at the intersections on the schematic means those lines are connected. No filled-in circle/dot at the intersection usually means the lines are *not* connected. What this means here is that the brown wire comes from J2, pin 2 on the MPU, down from the backbox to the playfield at one of those 8 switches. The wire connects to the *non-banded* side of the diode on the switch. Under the playfield, if you look closely at the diode on any of the switches on the switch matrix, you'll note one end of the diode has a band that may be gray or black depending on the type of diode. The diode is represented by the triangle with a vertical line on the schematic. The vertical line is the banded side. Always take care to correctly wire to components that use diodes--they are there to ensure the current moves only in one direction. Note again that the wire we are following connects to the non-banded side.
Once the brown/white wire reaches it's destination, it "Daisy chains" to the next switch in that same series of 8 switches on that vertical row. So you actually have 2 brown/white wires at most of the switches on that circuit--one coming from the previous switch, and one carrying the circuit forward to the next one in it's circuit. If a wire or diode breaks off the switch--breaking the "Daisy chain", it can disable other switches on the same vertical column or horizonal row.
I hope i did a decent job of explaining how the switch matrix works in simple terms. The solution here is to solder that brown/white wire to the switch's solder lug that's missing a brown/white wire. Look at the 8 switches on the diagram and see if you can figure out which one is being kept out of the circuit. It's possible there's a switch with just one brown/white wire attached and that loose wire needs to be attached to that same switch (completing the daisy chain between that switch and the next one in the circuit...note: they may not be wired in the same order as the diagram but that doesn't matter, as long as the wire reaches each one)... Take a look at how the other switches are wired and compare with the diagram. It'll take time to make the connections but it's all there. Just a matter of understanding what you're looking at and how to translate what you see on the schematic to what you see inside the game.
All that said: If you have a multimeter there are some very easy tests you can do to test the wiring from the connector at the mpu down to each of the switches on the playfield...
Follow up with any questions--i realize this is a lot of info.