Need more data on your switches. Post a data sheet for them, part number, and manufacturer name. Or, a picture of the terminals and the marking on them.
Kinda need a internal schematic to be sure. But, I'm guessing that the GND terminal is only for the internal led use. The internal switch contacts likely connect the + terminal to the led terminal, which would make it a single pole single throw switch.
The headlight, for example would have its gnd terminal connected to green in the harness. The switch would gnd would also connect to the harness green. The plus terminal of the headlight (either white low beam or blue high beam) would connect to the LED terminal. The black of the main harness would connect to the switch's + terminal.
I would check out the switch function with an ohmmeter, if I couldn't find manufacturer specifications for the switch. You need to know which contacts make a connection when the switch is activated.
The switch should also have a rating for contact capability. If it is rated from 1 amp, it's not going to last very long switching headlight current.
There are other ways the "LED switch could be wired internally. It may not have the internal resistor for the LED and require an external one for the LED to survive.
My assumptions could be wrong, as I have no accurate description of the switch you are using. There are thousands/millions of types of switches. The fact that yours aren't ordinary leads to far more uncertainty about what application the switches were intended to placed.
You should also specify what controls you are eliminating. So, we can tell what is left of the stock electrical routing. You should also make a new wire diagram for your bike, as, after you're done, no one will be able to tell you what broke, as it will NOT have any kind of standard connectivity.
Cheers,