I know this because I had to completely redo the AC on our Galaga.
power from the outlet goes through the cord, to the line filter, and from there will go to 3 fuses. from one of those 3 fuses, AC will reach the first transformer, which is the iso for the monitor, and then will bridge over to the next iso that runs various voltages to the original power supply board.
Arcadeshop typically has those ends that you crimp around the wire, kinda like an IDC where it will cut the insulation and grab the wire inside the end. from there that branches out to the new switcher.
if you would like to just skip that then you can solder 2 wires off the line filter or either the upper or lower pair off the first smaller iso to get your AC.
you're not altering the monitor's wiring in any way, and I think some people are confused as to what the "isolation" in isolation transformer means. it doesn't mean that the monitor is "isolated" from everything else or it'll blow up if it shares a connection with say the power supply or marquee light. no, an isolation transformer only gets rid of "neutral", so you effectively get a double hot alternating current instead. monitors that require isolation transformers will blow out the diodes and any other number of components depending on model if you run neutral to it.
so this is why Arcadeshop made the wires that you crimp around the existing monitor AC, it just needs an AC feed from someplace to power up.