Your concern for not wanting to mix up the battery voltage (54vdc) and the 5vdc regulated controller power and it's electronics is warranted. These wires must not be crossed
By switch, do you mean the one on the front of your display assembly? Where you press the power button to turn everything on?
Note: I see that the switch symbols are different from the reference below... Do you have a
separate power on switch?
At this time, using the display reference below, this is how I see parts of your system.
Your display/brake lever assembly has a 7-pin connector. Which would likely include these wires.
1) Batt+.....
Full battery voltage input, that when switched by turning on the display, goes to "key" wire.
2) Key (AKA Ignition or control) Gets
full battery voltage when display is powered up.
3) Ground... may be tied in with other components for their operation. Battery negative.
4) TX... Data transmit line. (low voltage electronic communication) intermittent voltage less than 5vdc when controller on.
5) RX... Data receive line. (low voltage electronic communication) intermittent voltage less than 5vdc when controller on.
6) Light positive power. Energized by light on sequence by display switches. Controller on.Typically, 5vdc or less.
7) Brake signal. Low electronic voltage signal, that when shorted to ground, stops motor output. 3.3vdc or so when controller on.
As you can see, a miss directed high battery voltage input to the wrong place would likely be very harmful.
Your throttle is also low voltage.
1) 5vdc controller input with controller on.
2) Ground (may be shared with ground above as mentioned.)
3) throttle signal (.8 to 3.6vdc typ.) with controller on.
Since you have a working controller with all exposed wires. You should be able to tell which is which by testing voltages.
Starting with the ignition "on" circuit. Then work thru and label off, light power, throttle power, ECT.
Then transpose those findings, to the original pinouts of the connectors if desired.
Being very careful to transpose one side of a connector (male) to the opposite side (female) because the pinouts will be mirrored!
For the minimal wires to #2 controller using one throttle and one brake input...
Power to "Key" wire. (Tied in with display "key" wire.)
Throttle signal. (Tied in with #1 throttle signal out wire.)
Brake signal. (Tied in with #1 brake signal)
Battery +
Battery -
Note: With controller #2's display missing and bypassed. Some switch functions will not be available. Obviously, PAS power setting for one.
Recommended precautions...
Keep all wires and test probes from touching.
Double check readings before connecting.
Perhaps put a 100mA fuse in line with the battery power control wire. May help if a mistake is made.
Any questions, or if I'm not clear on or wrong on a point, please let me know BEFORE wiring/trying!
Display reference used...
https://www.sharpbike.com/product/electric-bike-brake-lever-with-lcd-display-160pdd/