HOYLAKE, England >> With his thinning hair and his thickening waistline, Butch Harmon has a way of blending into the crowd when he follows his players’ competitive rounds on foot. On Saturday at the British Open, though, there was no missing him.

Early in the third round at Royal Liverpool, players whom Harmon teaches occupied the three spots directly behind the pacesetting Rory McIlroy: Dustin Johnson was holding down second, Rickie Fowler was third, and Jimmy Walker was tied for fourth.

By day’s end, Fowler stood second, six strokes behind McIlroy after posting a 4-under-par 68, his third sub-70 score, for a 54-hole total of 10-under 206. One stroke behind Fowler, in a tie for third with Sergio Garcia, was Johnson, who carded a 71. Walker was tied for 12th, at 5 under, after posting a 71.

Another Harmon pupil, Phil Mickelson, was 1 under and tied for 34th in his defense of the title he won last year at Muirfield.

Mickelson has won 12 PGA Tour titles, including two majors, since he took his considerable talents to Harmon in 2007. Fowler and Walker have been working with Harmon, a former PGA Tour player, for less than a year, and each has top-10 finishes in both of the year’s first two majors, the Masters and the U.S. Open.

Fowler was friends with Harmon long before they entered into a professional alliance, developing a relationship with him in the course of spending time with Mickelson, who has been a mentor.

For Fowler, the turning point came at last year’s British Open, where he played the first 36 holes in 12 over, 11 strokes worse than Mickelson, to miss the cut. Fowler, 25, has always been more a feel player than one consumed with technique. So it was not a good sign that he had a dozen swing thoughts rattling around in his head.

"I think he was a bit confused with his golf swing," said Fowler’s caddie, Joe Skovron. "I’d never really seen him like that."

Fowler hit balls on the range, and Harmon, as a favor, critiqued his swing. That was the start. By the end of 2013, they had formalized their partnership.

"When I first hit with Butch," Fowler said, "I was definitely probably at a confidence low as far as looking at my whole game."

He added: "But right now, I’m definitely able to come in the majors and go into each week believing in myself and believing in my game and believing in what I’m working on with Butch. And that gives me so much confidence, knowing that I’m working, I believe, with the best coach there is in golf."

Harmon, the son of Claude Harmon, the 1948 Masters champion, operates less like a physics professor than like an auto mechanic.

He has the ability to diagnose problems quickly and accurately, and most of his fixes are simple. He will tighten a swing, untangle the crossed wires in a player’s head and repair any leaks in self-belief.

"He understands how each person swings and delivers the ball," Mickelson said, "and he works with that, as opposed to trying to mold them to one idea. I think that’s why he’s able to work with guys so quickly and they do so well."

Mickelson won his first and only Players Championship, widely regarded as the fifth major, a month after he joined with Harmon.

Walker, 0-for-187 on the tour when he enlisted Harmon’s help, has won three of his last 21 starts.

And Fowler, who had one top-five finish in 16 majors before working with Harmon, tied for fifth at the Masters in April and tied for second at the U.S. Open.

For a second consecutive major, Fowler will play in the final group Sunday. He will be at ease doing so, he said, because of the work he has put in with Harmon.

"It’s kind of hard to explain," Fowler said. "It doesn’t feel like a big stage. It feels like I’m supposed to be here."

The fixes Harmon made to Fowler’s swing are minor; Harmon tinkered with his alignment and shortened his backswing. The results have been striking to Mickelson, who engages Fowler in money games on the Tuesdays of tournament weeks.

"He’s hitting the ball longer than I’ve ever seen him hit it," Mickelson said, "and he’s hitting more iron shots to gimme length every time I play with him."

Fowler had considerable ground to make up to catch McIlroy, whose six-stroke lead after 54 holes called to mind Tiger Woods, who led by the same margin going into the last round at St. Andrews in 2000. (Woods’ final margin of victory, over Ernie Els and Thomas Bjorn, was eight.)

Woods’ swing coach at the time was none other than Harmon. Since they parted ways, Woods has worked with Hank Haney and, now, Sean Foley and has overhauled his swing a couple of times.

On Saturday, as was the case all week, Woods’ driving was erratic, and it showed in his scores, which were all over the place. After opening with a promising 69, he shot a 77 and a 73.

Woods, who is coming off back surgery, has had his swing changes called into question repeatedly over the past decade — including on Saturday by Brandel Chamblee, a one-time tour winner and now a Golf Channel analyst, who said, "He willfully dismantled the golf swing that made him the best player in the world."

Woods won five times last year and was ranked No. 1 in the world in March. His swing is not exactly ready for the scrap heap.

That’s safe to say, but so is this: Fowler, Walker and Johnson have, in Harmon, a mechanic adept at preventive maintenance.

"He gives you a simple way," Skovron, the caddie, said, "to go play golf better."

Karen Crouse, New York Times