My 67 firebird won't start sometimes

My 67 firebird has a brand new battery and
ignition. The engine is completely rebuilt as well.
Ive had the alternator and battery testesd and they
work fine. Eveynow and then i will take the car to
run errands, it always starts initially. As I keep
turning it off and restarting it throughout the day
the car was eventually not start at all. It doesn't
make a click or turn over whatsoever but the lights
still work and the Speedo lights turn on. After 15 to
20 minutes the car will start again. I'm baffled as to
what the problem is.