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If the button doesn't work to lock out O/D, then the wires inside the shift lever are broken. This is very common, and also fairly simple to fix.
The first step when working on anything electrical is to disconnect the negative battery cable so you don't blow a fuse or kill yourself.
Pop off the O/D switch at the end of the switch lever and disconnect the 3 wires (keeping track of where each is connected).
Next you need to remove the gear shift lever: Put the truck in 1st or 2nd gear and you'll find a pin at the base of the shift lever that holds it to the steering column. It may be covered with a leather boot that has to be cut or pulled back to gain access.
When you remove the shift lever, it will expose the 3 wires leading up to the O/D switch. There are good odds that you'll find a hole worn through the plastic sleeve and at least one of the wires.
If you want a repair that will last, you'll need to replace all 3 wires with a thicker guage or protect them with a hard plastic sleeve at the base of the shift lever.
I don't think this is a fuse issue. I think O/D switch fuse is the same fuse used for the instrument panel so if it were the fuse, the panel would be out too.