The early HD internal throttles had a "push" cable that's solid wire. For chopper guys there was an aftermarket reversing linkage for a linkert so you could use an English type (or Barnett or MCM) throttle and external cable when you changed bars. The last of the HD internal throttles had a handlebar spiral machined the other direction for a "pull" throttle, used on the DC linkert, Tillotson and some Bendix carburetors.
HD did have the parts available to convert to left hand throttle and right hand shift (the Indian way.) This could maybe be the Chicago/police deal that Benny sorta remembers.
One guy in my club changed his bars and throttle, only never reversed the linkage. His throttle twisted the "wrong" way to go, and if you took your hand off, the spring would pull it wide open. He could ride it just fine. I tried it once around the parking lot, that was enough for me. This was in the early '70's.