No reverse gear why?

Hello,

There could be couple of reason for not selecting reverse.
First you could have an issue with the shift cable, over time the cable can stretch and that could make it difficult to engage certain gear.

I have attached the shift cable adjustment procedure. Please go through the steps and make sure that it is at the correct setting.

Another possibility is that the transmission shift engagement needs to be reprogrammed.
Follow this procedure:
Get the vehicle up to operating temperature. Make sure the transmission is over 130F.

Then preform, park to reverse for 8-10 times. Drive to reverse 8-10 times. Park to drive 8-10 times. And Reverse to drive 8-10 times. Be sure to wait at least 10 seconds between each engagement of the gears.
It is important that the transmission temperature stays above 130F for the duration of this procedure. With out the correct temperature the procedure will not work.
This should help the engagement of the gear properly.

https://www.2carpros.com/articles/automatic-transmission-problems

Please let me know of any questions.
Thank you.