It happened at the March, 1956 meeting of the Knoxville city council. Councilman Caswell Orton Walker (left in picture) got into a fistfight with Knoxville councilman J.S. Cooper. This picture appeared page 38 of the March 19, 1956 issue of the Life magazine.
Life magazine says that Cooper threw the first punch. He took a poke at Walker with his left. Cas Walker was fixin' to counter with a right cross but onlookers broke up the frakas before anybody could land a solid blow.
The magazine says the fight was over tax rates and property assessments (i.e. taxes). It's not known for certain but since Walker was known for being a fierce fiscal conservative it's reasonable to assume that he was fighting against a tax increase.
This event fifty years ago is a stark contrast to politics today when elected officials seem to never argue over a tax increase. They're too busy trying to figure out ways to slip over tax increases on innocent citizens so they can funnel cash their cronies and crooked buddies (ref. Mike Ragadale's shady wheel tax increase in 2004)