I think he served as Lt. Gov. from 1969 until the people of Texas kicked him out of office in 1973.
Interesting. That story is incorrect though when it downplays Barnes' role in the Sharpstown scandal. If you to some of the oldtimers and state legislators who were there during the thing they'll tell you Barnes was all over it. IIRC the two people who finished ahead of Barnes in his '72 governor bid were the eventual winner Dolph Briscoe - an outsider and moderate democrat in the race - and Sissy Farenthold, the liberal democrat. Farenthold was a state rep. The main reason she did so well was the fact that she had attained high statewide name ID as a leader in the "dirty thirty bastards" - a renegade group of state reps who blew the whistle on Barnes, Mutscher, and all the other Sharpstown cronies (the group was made up of the Republicans - who were fewer than thirty at the time - plus a couple disaffected Democrats including Farenthold). She was the anti-Sharpstown candidate in that race while Barnes was the undisputed Sharpstown candidate.