'66 Barracuda starts then dies right away

If it's dying when the key is in RUN, it sounds like you've got a bad wire or loose connection in the RUN circuit (or a bad switch which I doubt). I believe it's labelled IGN2 on the wiring diagrams and is the blue wire, not the brown wire coming off the ballast resistor, at least on the '69 diagrams. I know it's been bypassed but the wires are probably still there, just tied together. The bulkhead connector is the likely culprit, but with 40 year old wires, anything goes. If I've got my colors right, when the key is in START, the brown wire provides current to the coil and in RUN the blue wire does. Start by checking the bulkhead connector for burned or loose terminals. Once that's cleaned up and good to go, if it still won't run try running a jumper from the + battery terminal to wherever the brown and blue wires are tied together and if it runs in RUN, the problem is probably one of the wires so you'll have to check them all, but remember it still could be that bulkhead connector. I solved this one on my '69 by running a manually switched wire from the battery to the ballast resistor because 1) it was simple and 2) I got sick and tired of thinking it was fixed. Stuck it up under the dash and works as a hidden kill switch. Just don't forget and leave it on overnight.