The current limiter provides a way to ensure that the circuit plugged into it does not include a direct (dead) short, draw too much current and fry components, blow fuses and so on. It is possible that you could connect a circuit that does not draw much current and does not “light the light”. I have amps like that. I also have amps where the light glows brightly at start up, indicating a have current draw as the caps charge and tubes heat up, but then dims down as the amp warms up. Only when the light stay bright do you have an issue that needs corrected before removing the current limiter from the circuit.
BTW, remember to remove the current limiter from a circuit when checking voltages or setting bias.