I thought it was interesting Glen & Elvis recorded a lot of the same songs. We know Glen played guitar on the Viva Las Vegas soundtrack in '64. Glen also listed as a credit for playing guitar on a '95 cd box set titled Elvis-His Life and Music. Another small piece of trivia, he played rhythm guitar on Shelley Fabares #1 hit "Johnny Angel". That song hit it's peak around 4/62.
I know I didn't catch all of the recordings, but this is what I briefly came across in regards to the songs they recorded. Unless designated as a single, songs are listed on the represented albums.
Long Black Limousine
Glen's release-'63 Too Late To Worry, Too Blue To Cry
Elvis' release - '69 From Elvis In Memphis
Don't Think Twice, It's All Right
Glen's release - 2/64 instrumental album with Leon Russell (also sang it on the Goodtime Hour)
Elvis' release - 7/73 Fool
Tomorrow Never Comes
Glen's release-'63 Too Late To Worry, Too Blue To Cry
Elvis' release - '71 Elvis Country (I'm 10,000 Years Old)
Gentle On My Mind
Glen's release - '67 as a single
Elvis' release - '69 From Elvis In Memphis
Mary In The Morning
Glen's release - '67 Gentle On My Mind
Elvis' release - '70 That's The Way It Is
You'll Never Walk Alone
Elvis' release - '68 as a single
Glen's release - '70 Oh Happy Day
Until It's Time For You To Go
Glen's release - 8/69 Live - New Jersey
Elvis' release - 1/72 as a single
The Impossible Dream
Glen's release - 8/69 Live - New Jersey
Elvis' release - 6/72 Elvis As Recorded At Madison Square Garden
My Way
Glen's release - '70 Goodtime Album
Elvis' release - '77 as a single
Help Me Make It Through the Night
Glen's release - '71 Last Time I Saw Her
Elvis' release - '72 Elvis Now
American Trilogy
Elvis' release - '72 as a single
Glen's release - '84 Letter to Home album
I'm So Lonesome I Could Cry
Elvis' release - 1/73 Aloha From Hawaii Via SatelliteThere Goes My Everything
Elvis' release - 12/70 as a single
Glen's release - '75 Ernie Sings & Glen Picks
Some other songs that both have recorded:
Your Cheatin' Heart
And I Love You So
Words
I Believe
Oh Happy Day
Put Your Hand in the Hand
You Don't Have To Say You Love Me
Bridge Over Troubled Water
Oh Little Town of Bethlehem
O Come, All Ye Faithful
First Noel
Silver Bells
Tomorrow Never Comes
White Christmas
I'll Be Home for Christmas
Blue Christmas
Silent Night
In concert, Glen sang (among other Elvis songs):
Blue Suede Shoes
Love Me Tender
Can't Help Falling In Love
(Let Me Be Your) Teddy Bear
Loving You
You Gave Me a Mountain
Mike Morgan