Use a switch power supply:

http://a.co/bYKqI0u

You can hook it inside the cabinet (after the power switch), so no additional power wires are necessary. This will supply all the 12v you will need. You can also buy ones that supply both 12v and 5v if you have other mods.

I used one similar to this in my CFTBL, the 12v is already taxed on that machine.

You'll need to put the switch power supply in the circuit between the power switch and the transformer. That way, the power supply is only on when the game is on. You can remove some of the insulation on each line (don't cut the stranded wire), and wrap it around the screw terminal, Line (hot), neutral, and ground.

To attach your mod, yes, you'll need to cut the current connector off, strip the ends, and place them in the screw terminals of the switch power supply. Black is ground. Red is +12v. I've found that if you have a few mods to plug it it's much cleaner to get a power splitter for this. Pinball Life sells them (listed for stern machines, but can be used on any game).