Had the same problem in my 68 327 this fall. I have the original harness however not painless. We put a donor alternator on the motor for the first start. It ran fine but overnight the battery drained. I disconnected and tested everything and once all else was eliminated I took the alt to Autozone for a test, it was dead. Now it runs great 14V at idle!
1968 Camaro Z28 clone 327 .030 over, Muncie M20, DUI coil, Edelbrock Performer w/1406 , headers, 274 cam
1963 Chevy Biscayne-2 door, 283 2bbl, powerglide, Mallory Digital ignition
1985 Z-28 LG4, Edelbrock hdrs, Lakewood control arms