"Blue Eyes Crying In The Rain" was written in the '40s by Fred Rose; it was first recorded by Elton Britt and then made popular by Roy Acuff. In the '70s, Willie Nelson had a huge hit with it on his album Red Headed Stranger. It has also been covered by such Beck favorites as Hank Williams, Elvis Presley, and Olivia Newton-John.
Beck has performed the song once, on the second night of the giant 90th birthday concert for Willie Nelson in April 2023. (He performed a different song on the first night.)
So far, Beck has just performed this the one time. He was backed by the house band at the concert, which was led by Don Was. It included Mickey Raphael on harmonica and Greg Leisz on pedal steel guitar. You can watch it here: