But a simple gesture may offer a telling glimpse into the nature of their bond.
More than a decade ago, Cole and Higashioka, both Southern California natives, were scouted by Yankees talent evaluator David Keith. Keith, who also drafted former backup catcher Austin Romine, was the scout responsible for the Yankees selecting Cole and Higashioka in the 2008 draft.
It would take another 12 years for the pitcher whom general manager Brian Cashman has called his "white whale" to make his debut in pinstripes.
After declining to sign in 2008 out of Orange Lutheran High School, Cole had a brilliant career at UCLA. He was the Pittsburgh Pirates' No. 1 overall pick in 2011 and went on to become their No. 1 starter. The Pirates traded Cole to the Houston Astros in 2018, and he took his game to yet another level, becoming one of baseball's most dominant pitchers.
A week before Christmas last year, the Yankees finally landed Cole as a free agent, signing him to a $324 million deal, the richest contract ever given to a major league pitcher. And that investment has paid off so far, after the Yankees swept the Cleveland Indians in the Wild Card Series and prepare to face the Tampa Bay Rays in the ALDS, with Cole and Higashioka as their starting battery for Game 1 on Monday night.
Higashioka was the top baseball player at Edison High School in Huntington Beach, California, and part of an elite group of area prospects when he first played against Cole.
"I'm pretty sure I caught Gerrit, I can't even remember specifically when, but I'm pretty sure I caught him playing for the Angels scouts' team," Higashioka said in a phone conversation with ESPN ahead of Sunday's workout at Petco Park in San Diego. "I don't remember specifics, like what his pitches looked like or anything, but in California, if you are in that kind of prospect showcase, you run across everybody. You end up playing with or against pretty much everybody who is drafted."
A date that does stand out to Higashioka is Sept. 5, 2020, the first time he caught Cole in the big leagues, an occasion commemorated by a very special present for Keith. The Cole-Higashioka battery debuted against the Baltimore Orioles at Camden Yards, and during their pregame meeting, Cole told Higashioka of his plan to save the ball from the first pitch and present it to Keith.
"When we were going over the hitters, it was the first thing Gerrit said," Higashioka told ESPN. "He actually wanted the first pitch, but [Hanser] Alberto fouled the ball off into the stands. We couldn't get that one, so then we ended up striking him out and we kept that ball.
"But Gerrit was like, 'We should throw the first pitch back to the dugout so that we can send it to David Keith.' It's an amazing thought to have, especially, you know, we're going into a game, we're trying to win a ballgame, and it's the first thing he brought up in the meeting."
Cole also talked about the connections players make with scouts on Sunday.
"Those scouts are just often underappreciated," he said. "I think anybody that has a feel for the industry knows that, even on that side of the ball, the scouting department, they work together as a team. Obviously, when they're traveling to different games and such, as a kid, you see the same faces all the time.
"You know that earlier that day, or the day before, or the day after, they maybe [traveled] at some point an hour, two hours, three, four hours away, just to try to do their job and get some kids into professional baseball. They're kind of the boots on the ground and it's hard not to at least develop some relationship with them and be appreciative for what they bring to the game."
Cole has acknowledged that his comfort with Higashioka, who caught him in his last four regular-season outings, when Cole went 3-1 with a 1.00 ERA with 34 strikeouts over 24 innings, may have something to do with their temperaments and the ways they approach hitters.
"Probably because we're both from Southern California," Cole said before the Yankees' series against the Indians. "I mean, we have a lot of the same interests, and Kyle's ability to communicate, be a really creative thinker, good pitch framer, good pitch caller. So we've worked out well together."
"We have very similar personalities," Higashioka said. "For example, we are both very self-sufficient and are people that appreciate our alone time. But from a baseball sense, I think our thinking is pretty similar on the field in terms of how to attack guys. And it helps that I knew him a little bit in high school. That's another thing; it's always good to see a familiar face."
Higashioka stressed that sending the ball to Keith was but a small token of their appreciation.
"The scout that drafts you, you look at it as that's the guy that really believed in you from day one. Dave put his neck on the line for us," he said. "Anytime you are drafted, area scouts basically put their reputation on the line, saying, 'I think this kid is going to work out.' From day one, in 2008, when Gerrit and I were both drafted by the Yankees, it's probably what Dave envisioned, that one day I could possibly be catching him in the big leagues for the Yankees.
"Dave has always been just a genuine guy who really cares about the prosperity of the players, especially guys that he drafts. He just wants the best for us. But the funny thing is I think he originally drafted me thinking I would be more of an offensive player. I don't think he saw as much on the defensive side. And then when I got to pro ball, it ended up being the opposite, where I was more defensively inclined and the offense kind of struggled for a bit."
Higashioka said longtime trainer Steve Donohue, who has spent more than 40 years with the franchise and is the go-to guy for writing notations on milestone equipment, marked the ball as the first strikeout for the Cole-Higashioka battery, and added the name of the hitter, date and ballpark.
"Gerrit and I signed it on the other side," Higashioka said. "We mailed it, and Dave was pretty emotional. He told us we couldn't imagine how much he appreciated it."
The tandem passed their first playoff test with flying colors, with Cole striking out 13 batters and allowing only two earned runs over seven innings in New York's 12-3 Game 1 win over Cleveland in the wild-card round. Including the postseason, Cole's ERA with Higashioka behind the plate is 1.32, as he has allowed only five earned runs with an outrageous 47 strikeouts and only five walks over 34 innings.
"He definitely does his homework," Higashioka said with a laugh of Cole's in-depth knowledge of each hitter's particular weaknesses and strengths. "Sometimes in a meeting, he'll be like, 'This guy's got a 53% miss rate on changeups' -- a random stat that he pulls out of thin air. You really want that in a pitcher because he's doing as much as he can to get the biggest possible edge to win a ballgame."
Cole went 0-1 with a 4.96 ERA in three starts against the Rays during the regular season. He struck out 27 in those three starts, but the Rays batted .294 against the right-hander with five home runs -- two by Ji-Man Choi.
Yankees catcher Gary Sánchez was behind the dish for all three of Cole's starts against the Rays. Higashioka only faced the Rays once this season, catching Masahiro Tanaka. The Yankees lost that game 6-3 on Aug. 18, which was their first home defeat of 2020.
"We look forward to playing against the Rays. We didn't play well against them this season at all, so we're kind of chomping at the bit to get another opportunity to face them in this five-game series," Higashioka said. "This year their offense has been a lot better than in recent years, so they're definitely a tough lineup to navigate. And their pitching is superb. So the key is being aggressive with our pitchers, throwing strikes and just doing the little things right, because one or two wrongs can make the difference in these ballgames."
With the series being played at Petco Park in San Diego because of the coronavirus pandemic, Higashioka, as well as the other Yankees from the Southern California area, including Cole, Aaron Hicks and Giancarlo Stanton, hope to have their families in attendance. A limited group of family and close friends will be allowed to attend the games at the Padres' home ballpark, as was the case in the wild-card round.
"I'm still trying to figure out if they're going to allow my parents to go," Higashioka said. "That's what I'm hoping, that they will allow my parents and brother to come see the games. But then, you never really know how things are going to go. But hopefully."