The brown wire is for the electric clutch inside the transfer case
It is only used on 4WD vehicles(Rangers) with Automatic front locking/unlocking hubs
If you want to keep it then just get a single wire weather proof connector and make it a separate connection from the 8 pin connector
If you have Manual Hubs you may not needed it anyway
How it works
If you have automatic hubs that are unlocked then in 2WD the front drive shaft is not spinning, so the transfer case's chain drive and its gear on the output shaft is also not spinning
If you want "shift on the fly" from 2WD to 4WD with Auto hubs then there needs to be a way to engaged the gear and chain drive to output shaft without "grinding the gear"
The electric clutch, when engaged, causes gear/chain and front driveshaft to start spinning at output shaft RPMs and the gear is then engaged to output shaft, no grinding, then electric clutch is disengaged
There were 2 kinds of Auto hubs, 1997 and earlier used Torque Activated hubs, if the axles(driveshaft) were engaged(4WD) then the axle's torque/power would cause the axle gear in each hub to engage to the hub gear, locked
If put in 2WD the axles no longer have torque/power so the rotation of the wheel/hub caused the axle gears to disengage, unlocked
These were a little finicky for lock and unlock but did work and were "fairly" reliable if maintained
In 1998-2000 Ford used Vacuum activated Auto hubs
When 4WD was selected Vacuum was Pulsed to each front hub causing axle gear to engage hub gear, in theory the Vacuum was activated before shift motor moved to engage 4WD, but Ford left the electric clutch circuit in place
These were "fairly" UN-reliable
If you have Manual Front hubs that are left in LOCKED position thru the winter or when you think you will be using 4WD then front driveshaft, chain and gear will always be spinning at output shaft RPMs even if not in 4WD
So to engaged 4WD no Electric Clutch is needed, no grinding, because everything is spinning at same RPMs
In 2001 all 4x4 Ranger's got Live Axles, always LOCKED front hubs, so electric clutch was dropped, 2001 and up transfer cases do not have the Brown wire