That scene is, in my opinion, the best motorcycle chase scene ever filmed. I'm not sure who did the actual riding, but judging by the style displayed I speculate it's Bud Ekins and Eddie Mulder. Bud was Eddies uncle, at least he called him Uncle Bud, and it is widely known that Ekins broke "Squirrel" into the stunt Biz.
The bike "Coogan" is riding is a '67 Bonneville with the late model year paint scheme, which means it Probably has concentric carbs. It is missing the rubber knee pads that should be on the tank. The Bike the fugitive is riding is a '67 T100R Tiger. 1967 was the second year in a row that Triumph won Daytona with basically that bike, highly modified of course. The '67 Daytona 200 was won by Gary Nixon, and it set him up to go on and win his first of two consecutive Grand National Championships. In 1968 the T100R was dubbed "Daytona". I have both a '67 Bonnie and a '67 T100R, and I am fond of telling my friends that I have one of each of the model bikes in the "Coogan's Bluff" chase scene!
Another great chase scene is the Desert chase in "Hell's Angels '69" Mulder (on a TR6) and desert racer J. N. Roberts doubled the actors...what is amazing is that many of the actual Oakland Hell's Angels did their own riding in the chase! I consider it a close second to "Coogan's Bluff" in motorcycle chase scenes on film!
"Flattrackers go in deeper and come out harder!"...Or... "Racing is life, everything else is just waiting."...or... (With apologies to Gen. McArthur) "Old motorcycle racers never die...they just slip off the groove and fade into the dust."