Single wire reverse light switch for 68 Barracuda

According to my information, your transmission is the late '68 version, which uses the 3 wire neutral safety switch. As RedFish mentioned, it could have been converted at some point in it's history, but, I show it being originally a late '68 727 from behind a 340 engine. Around Feb 1, 1968 seems to be the date in which they swapped over from the single wire to the 3 wire switch. Your date code indicates April 1, 1968. Personally, I'd get a new 3 wire switch, a wiring pigtail for it, and just use the center wire on the pigtail to attach to your existing neutral safety wire. This assumes the transmission is unmodified, and that your backup light switch in the column works properly. Another option (one that may have already been made) is to use a manual transmission starter relay, or ground the neutral safety terminal on an automatic relay. Keep in mind that in doing that, the car will now start in any gear, which could be dangerous to those unaware of that modification.