I knew I had this book somewhere. " A Treasury of Railroad Folklore" by B.A.Botkin and Alvin F.Harlow.(1953). I have just scanned through the book and can find nowhere that gives a definite meaning for the word "rounder". However in the first verse of Casey Jones on page 54 the word "rounder" is applied to Casey himself.

Come all you rounders I want you to hear
The story told of a brave engineer
Casey Jones was the rounder's name
On a high right-wheeler he rode to fame

It then gives a biography of Casey and his brothers (all engineers) and Casey's wife Janey. The book does say that Casey was so devoted to his job that when he took a train to the Roundhouse, he waited personally to bring it back.

I suspect a rounder was a combination of a lot of things, all mentioned in the answers above, perhaps stating out as someone who took a train to the roundhouse and back or even drove both ways on a return trip. I can't imagine a inebriate being allowed to run a train, but in those days who knows?. Later the name may have been affixed to the hobos and drunks who waited at the roundhouse hoping for a free ride.

I will now have to read the entire 530 pages of the book just to satisfy my curiosity. Will let you know if I find anything.