To me, Old Time is the music my grandparents sang
Red Wing
After the Ball
In the Good Old Summertime
Wildwood Flower
Give My Love to Nell
A Bicycle Built for Two
The Man On the Flying Trapeze
When You and I Were Young, Maggie
Golden Slippers
Listen to the Mocking Bird
My Bonnie
Wait For the Wagon
When It's Lamp Lighting Time in The Valley
Billy Boy
Little Old Sod Shanty

I have the impression that Old Time music varies from region to region.

alice in montana