Voltage Regulator and/or Ballast fails

The charging system wiring should be fairly independent of the ignition. The only place they overlap is that they share the IGN feed from the key-switch. Since removing Vreg fixes your "no spark" issue, it sounds like the mis-wiring culprit so read below.

If your alternator has a single field terminal (male spade connector, termed "57 terminal"), then 1 wire should run from it to the "FLD" terminal on your Vreg. The case of the Vreg should be grounded to the body (and thus BATT-). The incoming IGN terminal is labeled "IGN", as I recall. There are electronic versions of this early Vreg.

But, if your Vreg has a triangular plug w/ 2 terminals, it is the later style (~1971+) and won't work with an early alternator. If they connected the "FLD" wire to an early alternator, that would short to ground to draw down the IGN source. That would disable your spark system, probably killing Vreg as well (solid-state usually dies shorted). When working correctly, the charging system should produce ~14 V (BATT- to BATT+) w/ engine running.

A few photos would have let us answer right away w/o speculation. Many posts here w/ good photos on both early and later charging systems. Search Google Images.