I reread your post . dont know how I missed it . just to clarify . you are saying that when using a light tester the light will come on when the points are open and then off when closed ?
Correct. It should blink when cranking. The points are a switch to ground. If the circuit is grounded the light turns out. The current is flowing through the coil to ground and the coil is getting hot. That's how you burn a coil out when you forget and leave the key on. At least you have a 50/50 chance! The spark happens when the points reopen.
If the light stays on the circuit is open. There is no ground so the current is waiting to go and it lights the light because it doesn't have an easier path. You can use a jumper wire to ground along the circuit and see where the light goes out. That's where the open is. Remember that spark happens when the points open so you shoud get a spark out of the coil when you turn the light out and then remove the jumper. You've just done the work of the points!
You can test the points with an ohm meter but you have to disconnect the wires and test at the contacts. Also test each contact to ground With the points open, One should show continuity to grround and one shouldn't. If neither showed continuity to ground, it would leave the light stay on even if the points had contact.