Welcome to 2CarPros.
There are two things to check. Considering the mileage, my guess is the linkage to the transmission range sensor is loose. So, I attached two pictures. One is the range sensor and the other a switch for the reverse lights. Based on which system you have, one or the other will be there. I circled both in the pictures.
Check for play in the linkage that doesn't full return the switch to reverse when it moves from drive.
Let me know what you find.
Joe
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Saturday, May 11th, 2019 AT 9:54 PM