FORT MYERS — It’s been 1,344 days since Rusney Castillo’s last big league at-bat.

Or about 32,000 hours; just under 2 million minutes.

In that time, Castillo has hit 38 home runs while batting .298 over 389 games with the Red Sox’ Triple-A affiliate in Pawtucket, where both McCoy Stadium and Castillo will celebrate their final year in 2020.

The PawSox will move to Worcester.

Castillo hopes to move to a city with an MLB team.

“Since 2014 I’ve known I have what it takes to play in the big leagues,” Castillo said through a translator at JetBlue Park on Wednesday. “I’m just focused on preparing and being out there with the guys. I know what I can do.”

The countdown is almost over. Castillo can see the finish line.

“Mentally, this year I came in really focused, locked in, especially since this is the final year of my contract,” he said. “Just trying to give my best to Boston and do as much as I can.”

Then he’s free.

Since he last sniffed the big leagues on June 16, 2016, when he struck out swinging against former Orioles pitcher Tyler Wilson (who is now playing his pro ball in South Korea), Castillo has cashed about $40 million in paychecks.

He’ll make another $14.3 million in 2020 until the contract he and former Red Sox general manager Ben Cherington originally signed in 2014 finally expires at season’s end.

“I’ve improved so much from when I got here,” he said.

Does he remember his last big league appearance?

“Yeah of course,” he said. “I’ve thought about it.”

Castillo is physically bigger and stronger now, at 32, than he was then, at 28.

He played in just nine games in 2016, but had a longer audition in 2015, when he hit .253 with a .647 OPS.

As a 33-year-old who will test free agency next winter, Castillo profiles as someone who would be fortunate to get a big league invite on a minor league contract, unless he has a monster year in Triple-A.

“My goal remains the same: I want to make it to the big leagues,” he said. “And if given the opportunity, give 100% to Boston. That’s the goal, to get up there.”

There’s always a chance, however small, it happens in 2020.

As currently constructed, the Red Sox payroll has about $16 million in space before it bumps against the $208-million luxury tax threshold, according to figures calculated by Baseball Prospectus. Castillo’s not on the 40-man roster, having been outrighted four years ago, and his contract does not count against the tax as long as he stays off the roster.

Let’s say the Red Sox are out of contention by July and trade a few big leaguers before the deadline. That would surely free up enough space for Castillo to be called up without the Sox suffering penalties.

He crushed lefties during his brief big league stint, hitting .309 with a .783 OPS in 103 plate appearances against southpaws. He’s solid in the outfield and pitchers like knowing he’s playing behind them, said Sox righty Mike Shawaryn, who has spent much of the last two years with Castillo in Pawtucket.

“He works hard enough to (be a big leaguer),” Shawaryn said. “I think he has the dedication, mindset and drive to do it. Obviously there are extenuating circumstances, but he has what it takes.

“You just watch him. He understands a lot of the game. I think from that aspect, having him in the outfield and having those young guys see how he works and hits, he provides a good beacon for guys to watch and see how he prepares.”

While Red Sox fans haven’t seen Castillo play in four years, he’s become a fan favorite in Pawtucket, especially because most of the best prospects in the modern game, like Andrew Benintendi and Rafael Devers, jump directly from Double-A.

“Exactly,” said PawSox president Charles Steinberg. “We had Devers and we thought, ‘Oh, we’ll have Devers for a while.’ We had him for a week. We had Michael Chavis at the start of last season and thought, ‘Oh, there’s a guy we can really get our arms around.’ He was gone and up to Boston (in April) and never came back.

“But it’s OK, you’re marketing the fan experience. But with Rusney, he’s been a dependable name in the lineup. … If you’re a good baseball fan, you know you’re watching a guy who has quite a story.”

Castillo has been a role model for younger players.

“I don’t think he’s ever denied any of the club things we’ve done,” Steinberg said. “He’s been a good teammate, a good fan connector, signs autographs and takes pictures. He’s quiet. I try to say hello in my broken Spanish. He’s very professional. Goes about his business and is a fun baseball player to watch.” Related Articles Gallery: Red Sox Picture Day

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