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I can't see the exact OHMs mattering as long as you have 3 different OHM readings as you turn switch to the 3 different settings, the 4x4 module would "know" switch has been turned as voltage changed
Cruise works the same way and of course blower fan
Any "clicking" noise would have to come from the 4x4 control module, it has the relays inside
Switch is just the 3 resistors, they can't make any noise, they can only make "magic" smoke
The switch tells the Module what driver has selected so it is just an "input" selection, it doesn't "power" anything, Module then powers the two relays to send 12v/Ground or Ground/12v to the shift motor on transfer case to get it to turn the correct way and to the correct position.
There is a sensor wheel inside the shift motor that tells the Module when motor is in the correct position for 2wd, 4high or 4low, Module cuts power then and turns on the Dash Light for that selection