Some Konami boards support Stereo audio. Rather than use the spare "audio" positions on JAMMA, Konami (along with many others) broke this out to a separate 4 pin header. Some TMNT boards have this while others do not. If your board doesn't have it, then you can only do mono audio, which is fine for TMNT.
For minimal invasive hackery, grab a 4 position pin strip (available online or at Fry's) and solder wires onto it and hook the cabinet stereo audio harness up to that. If your speakers are 8 ohms, you can put them in parallel, and if they are 4 ohms you can put them in series. Then hook the resulting 2 wires up to the JAMMA speaker positions and enjoy the Turtles theme in glorious mono (which is all it ever is anyway). It's possible that something like this is already available on your existing JAMMA harness, so check before modifying.
If you prefer, you could chop that 4 position connector off the wires and hook things up in a more permanent fashion, but then you'll have to undo it all if you want to go back to a stereo Konami board.