Okay, You will need to get a thottle cable (these can be found at motorcycle wreckers, bicycle brake cables or even old bonnet cables from cars > car wreckers) and a small blot, nut and washer.
1-Drill a small hole on that control lever, just big enough to fit the cable though.
2- Drill another small hole at the BASE of the blot, jus above the head.
3- Run the cable through the newly drilled control arm.
4- Put the bolt on the end of the cable going throug the control arm and tigthen the nut down onto the cable, acting as a clamp
5-You will now need to make a bracket to hold the cable casing
It should look something like this.

The thicker cable casing is held in the bracket, allowing the thiner cable to pass through easily..
You may be able to mount this to the tank, couling or even to the go kart itself.. be creative; it all depends on your engine.
One more thing, you may need a return spring, just simply hook one onto the cable/blot and hook to other end onto something making the thorttle return back to idle when you release the gas.
Good luck!!
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