Here is what your circuit should look like. I include an electronic schematic and a simple drawing of the circuit:
View attachment 473828
The idea here is that, when the "launch" push button is NOT pressed, the 1K ohm resistor and the LED are in series with the igniter. The 1K ohm resistor limits the current through the circuit to just a few milliamps. That is enough current to light up the LED, showing you that the igniter clips are connected correctly, but it is not enough current to actually heat up the igniter and set off the rocket motor.
When you press the push button, you create a "short" circuit through the push button, bypassing the resistor and the LED. Now the full current of the battery pack(s) is sent to the igniter (through the push button). This is enough current to cause the igniter to get hot. When the igniter gets hot, it sets off the rocket motor.
The LED will stop glowing when you press the push button because now the vast majority of the current in the circuit is bypassing the LED and flowing through the push button.
When you stop pressing the push button, the only way for current to flow is once again through the resistor and the LED. Again, only a small amount of current can flow. Since it is no longer bypassed, the LED comes back on.
The toggle switch in the circuit is just a simple "on/off" switch for the entire circuit. It serves the same role as the "safety key" in the Estes launch controller. Without the toggle switch in the "ON" position, the circuit is cut off and cannot operate at all.