Your wiring diagram looks correct
Well, I guess, your gonna have ta do some testin'
...& record the readings, for us
First, using a MM (multi meter) check the batt pack voltage
Then, connect the batt pack, to the controller
With the controller still switched "off" all plugs should show 0 VDC
...except the on/off plug (labeled "electric lock")
...& the charge port plug
(they both should show pack voltage)
Next, connect a switch to the "on/off" plug
...& switch the controller "on"
Now, with the controller switched "on"
...the Battery Indicator plug show pack voltage (of course)
...& the Indicator Light plug
...& the Brake Light (lever) plug
…& the Brake Light plug
(all should show pack voltage too)
The other control circuits
...the Reverse plug (labeled Astern) should show 4.6VDC
...& the 3-speed plug should show 5VDC/0 VDC/ 5VDC
(same as the throttle)
Then, let us know what your findings are
* The "arc" you see, when the power is first connected, is normal
...it's happens when the capacitators in the controller "draws power" to initially "charge up"