So the points may need to be gapped?
Yes, I would check to be sure that they are set to the correct gap. Adjusting the points will in effect adjust the timing of an engine. Too far out, and the engine won't start.
Using a .020 in feeler gauge, check the gap between the points with them at their maximum distance from each other. Their gap should be .020 in.
Just in case you don't know, slowly turn the engine flywheel while watching the points. You will see them open, and close as you turn the flywheel. When you see them just begin to move back toward each other stop turning the flywheel, and back it up just enough so that the points are again at their farthest distance from each other, then slide the feeler gauge between them. The feeler gauge should move snugly between them, but without any drag. Recheck the gap after tightening the adjustment screw.
And yes, one wire going into the points box, which is connected to one side of the points, along with the condenser wire.