No not necessary. Where did this tether come from? Are you sure purple is purple?
The gray wire to the tach is +5VDC and is double duty to one terminal of the smoke fan. The green is the return(control).
If purple is connected to the 12 pin as purple (Positive Voltage) it becomes one lead of the smoke unit element. The brown is the other (Control).
Normally there would be a light blue wire for the headlight.
You need to ensure that the brown and green wires you use in the engine is terminated on the 4 pin connector in the tender. Then you need to see where the purple wire goes to make sure it is Positive Voltage and not part of the headlight control. Picture of the engine close up would help.
You could use diodes off the motor lead to create your internal engine PV then use it to the heat element and headlight, then connect the current harness purple wire to the headlight for control, and make sure it is in the headlight position of the 12 pin. You could then have headlight control and everything else with out extra wires. Probably use the same bulb if the CV board is a 5 to 6V board. G