PORT ST. LUCIE, Fla. — They start lining up well before 8 a.m. — a dozen or so fans in Mets gear next to the players’ parking lot entrance five hours before the first pitch is thrown for a spring training game at First Data Field.

As Mets players drive in — some in luxury sports cars, some in pickup trucks, some in tricked-out Jeeps — the fans try to catch a glimpse, take a photo, maybe score an autograph.

The same thing happens hours after games. Fans try to get the players to stop on their way out of the parking lot. Some players do, some don’t.

One of the fans who stood vigil outside the players’ lot in the early days of spring training was 36-year-old Michelle Marie Thompson of Arvada, Colorado.

According to Port St. Lucie police, Thompson wasn’t there for an autograph. She was there on Feb. 26 and Feb. 28 looking for Tim Tebow, the Mets prospect and former Heisman Trophy-winning and NFL quarterback.

Thompson, according to police, claimed she was in a romantic relationship with Tebow. She had a sticker on the back of her driver’s license that read “I (heart symbol) Jesus/Tim Tebow.” She gave cops what she said was her address. It was Tebow’s home address in Jacksonville, Florida.

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On Feb. 26, police gave Thompson a trespass warning and urged her not to return. Two days later, she did, and was arrested and charged with trespassing, a misdemeanor.

The “victim of crime,” according to the Port St. Lucie police department’s incident/investigation report obtained by Newsday, was listed as “Tebow, Timothy.”

There is no indication, however, that Tebow and Thompson ever came into contact during the two days she was at the spring training complex. Tebow said Friday he would “pray for her.”

On Saturday morning, as fans lined up next to the players’ parking lot entrance, Thompson was in the Port St. Lucie jail, as she has been since her arrest. Unless she posts $750 bond, she will be there until her next court appearance, which is scheduled for April 7.

The news of Thompson’s arrest broke on Friday, just as Tebow was preparing to play in his second major-league exhibition game.

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After the game was over, Tebow was asked about his uphill battle to become a big-league baseball player. He was asked about what it felt like to hit against major-league pitchers.

He also was asked if he felt safe coming to work at First Data Field, which is traditionally one of the most open complexes during spring training in terms of fan access to players before and after games.

“Absolutely,” Tebow said. “I do.”

Still, the incident led to questions about how much access fans have to players at the Mets complex. Before games, or on days when there is no game, fans are allowed in at no cost to watch the players practice on one of the complex’s seven back fields. Fans watch from behind chain-link fences, but there are plenty of walkways that players use that are not closed off to fans.

It’s part of the allure of spring training — fans can get closer to players than during the season. It’s also what worries some players in terms of personal safety.

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“It’s very interesting,” Mets outfielder Curtis Granderson said on Friday. “You talk to different guys that come from other organizations the way they have their spring training facilities. A lot of guys go, ‘Wow, I’ve never had fans this close to me while I’m trying to work.’ Watching and being in the stands is one thing, but there are some places here where if you walk around, you kind of get a sense of, ‘Wow, they’re really close.’

“One, just for their safety and two, for ours, you are trying to still work and the same time they’re trying to enjoy and engage with you, but the timing of it isn’t always the best for it. A little interesting depending how the flow is working during the course of the day . . . It’s nothing against the Mets. It’s just the way the facility is set up.”

The closest of the seven back fields to the clubhouse and the players’ parking lot is Field 2. On Saturday, beginning at 9:30 a.m., about a hundred fans either lined up behind a chain-link fence or milled about the area as players went through stretching and other exercises before breaking into groups for other workouts.

“It’s just the way the facility is set up and every team is different,” said Granderson, who also played for the Yankees and Tigers. “The Yankees, there were times where you’re going from the stadium to the back fields, the fans are right there. There was a higher fence that divided them. The Tigers, the fans were typically not on the back fields unless there were games going on.”

Next to Field 2, a group of VIP fans wearing credentials around their necks — including, on Saturday, U.S. Rep. Peter King (R-Seaford), a longtime Mets fan — stood a few feet away from an area in which pitchers throw bullpen sessions. The crack of the fastball on the catcher’s mitt and the proximity to the pitchers leads to smiles and photos and brief interactions between fans and players.

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Chances are no one on Saturday was thinking about security or personnel safety. But it is a topic of discussion for the players when they first arrive to camp in mid-February.

“We have a security meeting once [spring training] starts here,” Granderson said. “The Mets personnel will say, ‘Hey, if there’s ever an issue, — like if you’re driving here because everybody recognizes your car [because] our parking lot’s visible — if you feel like there’s something going on here, turn back here to the stadium or call 911.’ That’s kind of the advised thing, but each situation’s obviously going to be a little different. But the big thing is hopefully try to not put yourself in any dangerous situation and know that you have some people to contact if you need to.”

The Mets have a lot of popular and well-known players, from David Wright to Noah Syndergaard to Matt Harvey to Yoenis Cespedes, and fans are always thrilled to get a glimpse or even a wave from the stars.

But few athletes attract a following like Tebow, who is wildly popular in Florida from his exploits at the University of Florida. Tebow’s workouts, whether with the major-league players or on the minor-league back fields, always draw a crowd. Tebow tries to engage with as many fans as he can, especially the young ones.

“I think to be able to encourage someone, makes someone’s day, put a smile on their face, means so much,” Tebow said on Friday. “You want to be bigger than whatever game that you’re playing. At the end of the day, if all you’re able to do is win or lose games, get a hit, strikeout, whatever it is, it’s fun, it’s a passion, that’s great, but at the end of the day it’s just a game. You want to be able to have your life be bigger than a game, be more than just a game. I think being able to try to encourage and inspire, put a smile on someone’s face, I think that’s a big part of it.

“So, for me, it’s not like you can do it all the time, see every fan. That’s not realistic. But you can try to make someone’s day every day and that’s something that I look forward to and you try to find the right people to do that — preferably they aren’t selling something on eBay — but try to find the real fans out there and thank them for their support and try to put a smile on their face.”

Tebow said the arrest of Thompson did not make him change anything about his routine or worry about his personal safety in his first baseball spring training.

“I just try to focus on the next thing,” he said. “At the same time, I wish her the best and just pray for her. Want her to get as much help as she needs as possible. But at the same time, as an athlete you learn to try to compartmentalize. It’s not always easy, but it’s something that you have to try to do.”

In November, the Mets and St. Lucie County announced an agreement on a $55-million upgrade to the minor-league complex and a 25-year extension of the team’s lease. The Mets have held spring training in Port St. Lucie since 1988.

“We are excited about the modernization of the facility, which will significantly improve the fan experience,” Mets COO Jeff Wilpon said in a statement at the time. “St. Lucie County will remain a destination for hundreds of thousands of Mets fans for years to come.”