|Alfredo Barba Mariscal|
There are competing theories for who the linchpin of narco political influence is within Jalisco. I personally suspect that it's Alfredo Barba Mariscal. Barba is the union secretary for the Confederacion de Trabajadores de Mexico (CTM Labor Union) in Jalisco. He's also the secretary of Tlaquepaque, a political position in one of the five municipalities that make up Guadalajara. Arguably Tlaquepaque (Mayo turf) is one of the two most important of the five.
Barba is closely supported by Raul Flores Flores and was a gambling buddy of Luis Rodriguez Olivera. They've been to Las Vegas together more than once. A couple of years ago when Barba went to Las Vegas, he lost $30 million and his father paid his debt.
Raul Flores gained his fame when he gave Joaquin Guzman Loera (El Chapo) money after he escaped from prison, and helped him get on his feet. Chapo never forgot the favor. Flores usually maintains a very low profile, though some of his employees (other than Luis and Esteban Rodriguez Olivera who are now in custody in the US) such as Jose Tierso Martinez Sanchez live the life of big time narcos in Colombia, Brazil and Peru these days.
There is Jorge Aristoteles Sandoval, Mayor of Guadalajara, as well who should be in the running, but he's gone off on his own and trafficks with other political figures (paying tax to the Sinaloa Federation). He's a useful tool, but doesn't have the sort of stroke that Barba seems to have.
Honorable mention goes to Arturo Zamora Jiminez, PRI candidate for governor of Jalisco and close associate of the infamous narco attorney, Jose Julian Jordan Gonzales. He's viewed for "being so crooked that he's round" and as a useful tool rather than a man with real power.
Of course, all of this is simple idle speculation. Merely my opinion.