I think that the LED is connected to one of the switch pads (negative) internally to the switch therefore you have 4 wires instead of one. but to prove this you need a multimeter.
Your switch has to have 3 pins. The Fechter/Vedder anti-spark uses a SPDT switch (single pole, double throw). The negative of the LED is wired to the negative of the anti-spark switch
Don’t hook up the positive of your LED to the positive of the anti-spark without an appropriately sized resistor, unless the LED is rated for that voltage. Many of the LEDs in those switches are only 12V or 24V, and can’t be hooked up to full pack voltage. I recently switch to a 220V LED switch, which works well for 12S at ~50V (not super bright, but also not dim)
If you dont mind having the regular switch and not the round one. And you care about the LED indicating that the board is on, it would be easier just to wire the LED and a resistor in series to the output of the switch and have the LED as a “separate” unit.
I will throw that in the package for you both the LED and the resistor of appropriate value. Just tell me what battery pack you are using so I can calculate the value