What's your battery voltage and how old is it? Is the starter new? Usually a "click" is a bad starter/selenoid or battery without enough *****. If the battery is ok then try hitting the starter with a hammer, and no im not joking. Sometimes a good wack can free up a stuck starter.

 

 

Where is the "click" originating from? Have you done the obvious and checked the fuses and relays?

 

 

The Click is the PCM relay, and it should click with key on, that powers up the PCM(computer) and most other 12v engine components, like injectors and spark system

1999 and up V6 Rangers will have PATS(passive anti-theft system), so the 2001 engine fuse box will have a PATS starter relay in it, the PATS computer must GROUND this relay for it to work.
If you swapped out the computer for the engine swap then you will need to GROUND this relay permanently, which was normal on the 4cyl Rangers without PATS

As far as the 12v activation goes for starter motor.

For automatics:
Ignition switch in START(12v)----------------(fuse 24/cab fuse box)----------Clutch bypass--------------------DTR sensor----------------------------starter relay in engine fuse box

For manual trans:
Ignition switch in START(12v)----------------(fuse 24/cab fuse box)----------Clutch switch-----------------------starter relay in engine fuse box

Clutch bypass is just a connector plugged in where a clutch switch would have gone, and passes on the 12v to the DTR
DTR is digital transmission range sensor located on the drivers side of transmission, shifter must be in Park or Neutral to pass the 12volt to starter relay