Neil only recently saw that footage for the first time, joking with his dad that he would have no trouble hitting him. Tom chuckles at the notion.
"I wish my career could have gone on long enough so my kids could have seen me play," he said while watching Neil earlier this week from the Citi Field stands. "But that wasn't the case. I had some health issues, arm issues which were all built around arthritis, and my career came to a halt way too early."
Arthritis nearly cost Tom more than just his baseball career. About 10 years ago, trying to work into better shape for his daughter's wedding, Tom -- who has had multiple hip and knee replacements -- visited a doctor with what he believed to be a routine injury. He received an injection, which resulted in an infection.
"I was a sick man," he said. "To be honest, I am lucky I'm alive."
Reticent to burden Neil as he worked to make his big league debut, Walker kept his illness secret from his son. It was not until early in the Minor League season when Tom drove two hours from Pittsburgh to Altoona, Pa., to watch Neil play that he realized something was wrong. Confined to a wheelchair, Tom was nearly 60 pounds lighter than when Neil had last seen him.
"He was in shock," Tom said. "He had never seen me sick. And I had never seen myself sick like that, either. But the good Lord had other plans for me, and left me here to do better things."
From an early age, it was obvious that Neil had inherited his father's love of baseball. Yet arthritis robbed Tom of the ability to interact with his son on the diamond in the usual ways. By the time Neil began advancing up the Little League ladder, Tom could not throw batting practice to his son, nor hit him ground balls.
Instead, the elder Walker found other ways to nurture his son's passion. A coach for all of his children, Tom became proficient at teaching. He shuttled Neil to and from the baseball field. He instructed him on the nuances of the game.
One afternoon, fearing that a lack of players would force him to forfeit his oldest two sons' American Legion game, Tom asked 9-year-old Neil if he would be willing to play alongside his 15- and 17-year-old brothers. The future Major Leaguer did, catching the opposing coach's attention when he made a difficult catch in right field.
"No matter what, if my older boys played, after the game was over I had to take him and put him on the field and let him take batting practice, or he wouldn't get in the car," Tom said, laughing. "I just learned to say, 'Honey, we'll be a little late.' And she got used to that."
These days, Tom's wife Carolyn is typically alongside him when they make one of several pilgrimages per year to New York, Washington or beyond in an effort to watch Neil play. Because their other children planned a fishing trip for Tom on Father's Day weekend, the Walkers drove from Pittsburgh on Monday to spend a few days in New York City.
Neil, who went on the disabled list Thursday with a left hamstring tear, became a father himself for the first time last August. With that, he gained a newfound appreciation for the sacrifices his father made when he was younger.
"I never remember a time that he didn't have time for us, that he didn't have time when I asked him to come give me some flips off the tee or take me to the field," Neil said. "With all that he's gone through, he never complains. I've got to pry out of him how he's feeling. He never wants to ask for help or anything like that. So I try to instill some of those things in myself."
Tom believes he could have played longer in the big leagues, in spite of his arthritis. He decided instead to concentrate his energy on creating the family he cherishes today.
"I've seen it pay off in every one of our children," he said. "To see Neil play as long as he has at this level, that's a blessing. That's a nice blessing for me."