First look at poor ground contact. Be sure both contacts are clean.
Then check the switch at the bottom of the steering. Some time the contact can get bent on the bottom, or the contact plate is not pushed up tight enought into the switch cover.
Next time this happens, or anytime really, have someone at the front and rear of the car and wiggle the switch housing and see if you can correct, or recreate the problem.
Usually if is is grounding, the engine will also respond by not running smooth. You don't mention that.
If you have not done so in your restoration, purchase another of the thick cable that runs from the negative pole of the battery to the starter switch, and run a cable from the postitive terminal to one of the transmission bolts for an extra ground.
Next thought, did you install a fuse? If not, do it. If you have one, some are very flimsy made, check to be sure the fuse in not lose, or the contact bad, or the connection; or even the fuse unit is not the cause.
If you are new at this, understand touching the fuse and contacting the car is very painful. Use a piece of wood (I use a chopstick) or something insulated whenever you touch it.
When all else fails, disconnect everything, then reconnect one thing at a time, and check with a miltimeter or test bulb. This happened to me, and it turned out to be the brake switch. The connection for the power to the switch has the contact on the inside of the switch. When I tightend the bolt, it turned the contact so it was now close to the cover, and I was getting an arc, causing my lights to dim.
If none of this works, just drive during the day.
Good luck