Young Francisco would follow big Francisco around as the man played in various Mexican leagues with a passion that far exceeded his talent level.
"I became a catcher," Rodriguez said, "because he was a catcher."
Like his padre, the lean and lighthearted son wasn't much of a hitter -- although he did have his moments.
"I played in five international tournaments in Little League and [Senior] League from [age] 7 until 16," Rodriguez said. "And I made the [All-Star tournament] team in four of them."
In a Senior League tournament in Ecuador when he was 16, Francisco and his team squared off against a Cuban squad whose star was a manchild who dominated games with the bat and his right arm. Kendry Morales could do it all.
"You don't forget a guy like that, with that kind of ability," Rodriguez said. "He was hitting bombs, throwing heat. They beat us in the championship game, 5-3. I made the last out.
"I came up with two outs and two on. Kendry usually played first base, but he would come in and pitch, too. He was nasty -- 93, 94 mph with a dirty split, a slider.
"He threw me a heater, first pitch, and I pulled it foul by about 15 feet. It would have been a game-winning homer. He threw me all breaking pitches after that, and I grounded into a force out to the shortstop."
That was 1999. Eleven years later, Morales and Rodriguez are employed by the Angels. While it's been a season Morales would like to forget, a grand-slam celebration at home plate having gone terribly wrong, it's been one Francisco always will remember.
Seemingly buried on the depth chart as one of a handful of Rodriguezes in the organization, Rodriguez came in out of the shadows in his fifth professional season to give manager Mike Scioscia durable, consistent work out of the bullpen.
His journey from modestly talented catcher to big league pitcher is a remarkable one.
It started when a Tampa Bay scout held a tryout in Vera Cruz, Mexico. He took one look at Rodriguez throwing 89-90 mph from his knees to second base and told him he should think about trying his hand at pitching.
"I'd never pitched before, but I thought, `Hey, why not?'" Rodriguez said. "I started pitching when I was 20 and had no mechanics at all."
What he had was desire, an inherited love of the game from his father.
The Rays' scout never made it back to check on Rodriguez, but another scout, working for the Angels, knew of his talent. Bobby Magallanes -- now managing at Double-A Arkansas -- had played on a Mexican summer league team with him in 2001 and recommended Rodriguez.
Rodriguez was 21 when he was signed by the Angels as a free agent the day after Christmas in 2005. He began his career with high Class A Rancho Cucamonga in '06.
"I could throw hard, but that's about it," Rodriguez said. "I had to learn everything else along the way."
Two years in the California League resulted in growing pains (he was 9-21 combined with 5.47 and 5.96 ERAs), but the organization liked those radar gun clockings in that 94-98 mph range -- and his unflappable makeup.
Rodriguez is neither easily discouraged nor intimidated, qualities you can't teach.
Gradually, it began to come together, the breaking stuff and changeup complementing that premium gas. Elevated to Double-A Arkansas, no longer a starter, Rodriguez was 5-5 with a 3.82 ERA in 2008. He was striking out almost a hitter an inning (69 in 75 1/3 innings).
Next stop: Triple-A Salt Lake, in 2009. His progress continued, reflected in a 5-4 record, 3.96 ERA and 60 K's in 77 1/3 innings.
Two other right-handed Rodriguezes -- Rafael and Fernando -- ranked higher on the depth chart. But when opportunity knocked this season, it was Francisco who answered.
Summoned from Salt Lake by the Angels on April 15 in an emergency role, Rodriguez debuted at Yankee Stadium with a perfect inning of relief. He was sent back to Salt Lake, returning to the Angels in late May.
He continued to retire hitters, going 9 1/3 innings with 11 strikeouts and only three hits allowed before yielding his first big league run.
A workhorse, he has appeared in 34 games covering 40 1/3 innings, going 1-3 with a 3.57 ERA.
"This has been an amazing season for me," Rodriguez said. "I want to do whatever I can for this team.
"In a way, I'm lucky I didn't start pitching earlier. I've had no arm problems. I don't even ice after I pitch. I can throw multiple innings, and I can throw two or three days in a row, no problem. I like the competition. I love being able to face the best hitters in the world."
If Scioscia needs a pinch-runner in a long game sometime, or even a guy who knows how to strap on the catching gear, Rodriguez wouldn't hesitate to volunteer.
"Mexicans aren't known for their running speed," he said, laughing. "But I was a track and field guy when I was young. I ran the 400 [meters]. My best time was 46.92, when I was 20, 21."
He has justified Scioscia's faith in his ability to bring the heat and take the heat while serving as a source of good humor and encouragement for teammates throughout a disappointing season.
When he was credited with his first Major League win on Saturday in Minnesota, the same day Peter Bourjos hammered his first big league home run, Rodriguez didn't even know he'd picked up the victory until a beat reporter informed him.
"That's nice to know," he said, having gone 2 2/3 innings in relief of starter Trevor Bell. "But what matters is we won a big game. This is all about the team."
He wasn't expressing the company line or being politically correct. It came straight from the heart.