All that stuff you said you did--and nowhere did you say you even looked at the ignition system, which is one of the FIRST things I would have looked at. A 1959 has bad (cracked) coils, unless somebody has already replaced them. In any case, you are wasting your time till you verify their conditon. Also in there are the breaker points and condensers. If the points are worn or greasy, it isn't going to run right.
The wires go to a pair of mercury switches. That is mercury--as in the metal, not Mercury as in outboard brand names. One of them prevents starting the motor when the throttle is advanced too far. The other one prevents the vacuum cut-out switch from operating at other than slow throttle settings. You will find that the wires cannot be re-soldered to the posts because the posts are stainless steel. The wires originally were welded on.
