Check out the gait/limp/jakewalk of Walter Brennan in the Bogart & Bacall film To Have And Have Not. I don't know if it's an accurate depiction of the walk but it's there for sure.

Back a few decades, STASH RECORDS put out an LP called JAKE WALK BLUES. It was all songs concerning Jamaican Ginger.

Side one:
Jake Walk Blues (the Allen Bros.)
Jake Leg Wobble (Ray Bros.)
Jake Legs Blues (Byrd Moore & the Hotshots)
Jake Leg Blues (Willis Lofton)
Limber Neck Rag (Narmour & Smith)
Jake Walk Papa (Asa Martin)Bear Cat Papa Blues (Gene Autry)

Side 2:
Jake Liquor Blues (Ishman Bracey)
Jake Bottle Blues (Lemuel Turner)
Got the Jake Leg Too (Ray Brothers)
Jake Leg Blues (Mississippi Shieks)
Jake Leg Blues (Maynard Britton)
Jake Leg Rag (Narmour & Smith)
Jake Walk Blues (Maynard Britton)

All of the songs were from 78s issued 30 years earlier.

Art Thieme