In the schematic you will see there IS a relay involved, but it is only used to engage a clutch in the transfer case to bring the shaft up to speed for a smooth shift. Its failure will NOT cause it to fail to shift, but it will make it clunk at speed. You’d have to lay on the DS floor, looking up under the center of the dash to find that relay box. It also contains the Battery Saver relay, but I wouldn’t bother. I really think your 4X4 Control Module is bad, if the fuses are good. I can’t tell you exactly where that is located, but the diagram shows it in the center of the dash. I’d expect it to be behind the radio/heater controls area, on the right? It has a label that says 4X4CM and is approx. 6” x 5” black box, with two connectors. It’s mounted with two screws.
Your e-mail Spam control filter blocked me from sending the schematic. I can't get approved (from your link) because the work server refuses that connection. I'll send it to my hotmail address (Earl43P@hotmail.com) and send it to you from home at lunchtime.
2000 2.5 MO5D 4.10 one-wheel drive DD - gave to my older son
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2000 3.0 4WD M05D 4.10 S-cab Off-Road package with 235-75-15" tires, hotrod DD, lol