Transmission - no reverse

If it was the transfer, it would not go forward. Probably trouble with the reverse band or clutches.
https://www.justanswer.com/car/3ndyu-2000-gmc-jimmy-will-not-go-reverse-every.html

If your fluid level is right you may have a bad transmission. you need to talk to a mechanic.

Nope.

May be some shift solenoids issue. Do you have a service engine light on? If so that will tell what solenoids may be faulty. The shift solenoids are inside the transmission pan and bolted to the bottom of the valve body.

Does it also hold first gear longer that it should and then shift right from 1st to 3rd? It sounds like you broke the sun shell in the transmission. The trans will need to replaced or rebuilt.

It winds up in 1st and then shifts right from 1st into 3rd. Then never shifts into 4th. Plus rev is gone. You broke the sun shell. The transmission will need to rebuilt or replaced.

transmission!!

Check the automatic transmission fluid color.

It should be lite pink and there is ZERO odor of burn friction material.

TOP OFF is it's low on ATF

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Have some one the check on the reverse light when you put the truck into the reverse gear.

NO reverse lights then the neutral safety is falling.

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Check for free play on the gear lever. Pay close attention on the transmission end.

USE clear to remove excess dirt.

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Inspect transmission pan and the floor for ATF leak.

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Cheers,

MUSTGO.

The transmission needs to be serviced and repaired. There is an internal switch or solenoid that has gone bad and needs to be replaced.

reverse band is a goner