The power to lights, ignition use a wire from the same lug on the starter switch that also has the positive battery cable. If the wire in on the other starter switch lug then lights and ignition will only work when the starter switch is closed. Also be sure that the wire goes to the ammeter, the ammeter is functioning {needle moves) and and the other terminal of the ammeter is connected to the light switch and ignition switch.

I don't understand  "starter switch closed".  The starter turns over great!  How can I use a test wire to see that I am getting power to the ignition, lights, etc.? Could it  be the foot button on the  starter connection?  Could it be that the rebuilt starter was put together wrong?  

@arthur-c-winters I'm not familiar with the wiring on that specific car but in electrical terms, a "closed" switch means the circuit is complete while an "open" switch means the circuit is broken. For example, when you flip a switch to turn on a room light, you "closed" that switch. When you turn the light off you "open" the switch.

How can I find out what the problem is and fix it? How to short circuit so I can see where the problem is?

Again, I don't know the specifics of your wiring but as a general rule you start where you have power (each wire individually, yes electrical problems can be a real hassle) and trace that wire connection to connection until you lose power. Somewhere between the have and have not is where your problem lies. Sorry I can't be more specific. Hopefully someone with personal experience with your vehicle will chime in.

Here's a process for checking the ignition circuit that Chipper put together: Notes from Chipper. I hope this helps. This is a copy of a post in the old VCCA Forums. ( https://vccachat.org/ubbthreads.php/topics/285347/re-1950-wont-start.html#Post285347 )

You can check most of the ignition system before trying to start the engine. Connect positive post on battery to positive post on coil. Or you can turn on the ignition switch then remove the wire from the positive post of the coil. Quickly pass the terminal end of the wire past a ground to see if you get a spark. Or if you have a VOM or test light you can test the positive post on the coil with everything attached and a piece of paper between the points. You should get battery voltage or light the test light if the wire, ignition switch and battery are good. If no spark or voltage then check the switch, wires or battery. Once you have power to the positive post on the coil then you can test other components.

With the paper between points (or points open) you should have battery voltage on both coil posts and to the hot side of the points. If not check wires and terminal ends.

Once you have voltage to the points short across the points with a screwdriver. You should see and hear a spark. With spark at points, hold the end of the center coil wire approx. 1/2" from ground and short across the points. You should get a spark from the end of the wire to ground that makes a "Snap". If not check the condenser to see if it is attached to the negative post on the coil or wire to the points on the distributor and the case is grounded. If not spark or weak spark replace the condenser. Once you have a strong "snappy" spark from the coil center wire, test the points. Remove the paper from the points and open and close then by hand. If you get the same strength spark as shorting across them they are good. If a weaker spark, clean or replace the points. Once you have a good strong spark from the center wire operating the points, put on the rotor, distributor cap and center coil wire to the distributor cap. You are ready to start the car.

As you can see it does not take a second person to test and diagnose the ignition system with a set of points. Don't have to turn over the engine either. If there is a problem with the engine starting or you have any doubts that spark is getting to the plugs it may take a person to hit the starter while another person holds a spark plug wire 1/2" from a ground. It can be done by a single person on a '29 to mid-30s Chevy by activating the starter switch with the left hand and holding the wire with the right. If your left hand is weak it also can be done by switching your hands.