Hi, Crazy Joe.
First of all, welcome to the boards!

Extremely hard to know for sure who this "Jack the Barber" might have been. However, I know of one "Jim the Barber" (real name James Rubertone 1902-1966) who was a member of the Colombo Family.
He briefly served as an acting capo on behalf of Ambrose Magliocco in 1964. Employed by the Truck Rental Coporation, owned by the Magliocco brothers. Rubertone was active in shylocking and crapgames. He seems to have operated out of the Bensonhurst section of Brooklyn and lived someplace near the 70th street, according to informants.
He was very short, had dark hair and wore eyeglasses.

Does this ring any bell?

Joe Gallo and his older brother Larry, were both soldiers in the Colombo Family. There are some indications that Larry however, was given a capo spot by Joe Colombo as part of a peace treaty between the warring factions in the Profaci/Gallo war. Larry died in 1968.
The third brother, Albert was later inducted into the Genovese Family.