It could be forgotten in the grand scheme of things, but Frank Gore’s touchdown was special in ways beyond the New York Jets’ realm.

In the photo archives of the New York Jets, the images of Frank Gore adorned in green will probably be stored in the same folders as LaDanian Tomlinson, Matt Forte, and even recent departee Le’Veon Bell. They’ll no doubt prove popular in the never-ending Twitter trend when someone facetiously speaks of legends of the game through an identity they’re almost never associated with (i.e. “Boston Bruins legend Brian Leetch” or “Seattle SuperSonics legend Patrick Ewing”).

But Gore is leaving an impact on the modern Jets through his continued rushing exploits. With Bell having moved on to Kansas City, Gore continues to carry the heaviest rushing burden, a trend that continued in their latest endeavor on Sunday against the Los Angeles Chargers at SoFi Stadium. Despite the winless Jets falling in a 34-28 final, Gore managed to end a personal streak of despair, scoring his first touchdown of the season on a one-yard plunge in the second half. He finished the game with 61 yards on 15 carries, his best output in the former since a season-best 63 during Week 2’s loss to his most well-known employers in San Francisco

Gore’s touchdown was special in the fact that not only has he now scored in a third NFL decade…he’s now tied with Edgerrin James for 20th-most on the all-time NFL rushing touchdown ledger at 80…but also in the fact that he was not the only man named Frank Gore to earn a touchdown over the weekend.

This weekend marked the first time that both Gore and his son, Frank Jr., each scored a touchdown on the same game schedule. The younger Gore earned his score on Saturday during college football action, representing the University of Southern Mississippi, a 51-yard tally through during the Golden Eagles’ tilt against Texas-San Antonio. It was the second score of the season for the freshman Frank Jr., who also had a rushing touchdown in USM’s win over North Texas on October 3. Gore Jr. also earned his first career triple-digit yardage output with 130 on the ground.

Unfortunately for either Gore, their efforts weren’t enough to avoid the cold reality of defeat. USM fell to UTSA by a 23-20 final while Gore and the Jets couldn’t muster up a comeback effort against the Chargers. The loss officially eliminated the Jets (0-10), who trailed 24-6 at halftime, from playoff contention.

The elder Gore wasn’t keen to focus on the positives on display in yet another defeat and spent his postgame comments focusing on the unfortunate reality that the Jets are careening towards becoming the third team in NFL history to post a fully imperfect 16-game season (joining the 2008 Detroit Lions and 2017 Cleveland Browns).

In the process, Gore, the third-leading rusher in NFL history, brought up an unfortunate reality: 2020 could be his final season in the NFL.

“We’re thinking about (0-16) every day,” Gore said, per Rich Cimini of ESPN. “We’ve got to get one. You don’t want to go 0-16, especially (since) this might be my last year. I can’t go out like that.”

In other words, don’t expect Gore, 37, to go along with the notion of tanking that Jets fans so desire to secure the top overall pick in next spring’s draft. He certainly knows what it’s like to go through a rebuild: upon joining the 49ers in 2005, it took Gore seven years to enjoy his first winning season, one that ended in the NFC title game against the Giants. The team made the Super Bowl a year later, partly in thanks to Gore’s magnificence on the field.

But, in another cold reality to both Gore and the legions of fans he has built up through his longevity, the running back knows that his time is limited on the NFL circuit. It’s clear also that Gore is removed from his prime, as evidenced by a 3.6 average carry that’s tied for the career-low he set last season in Buffalo.

“I’d say it’s tough because it’s the stage of my career,” he said in Cimini’s report. “I was younger in San Fran and I always felt like, ‘I got time, I got time.’ Now, I don’t know if I’m going to play next year and…I don’t know. You just never know. I’ve got to be real with myself, how teams think about my age. They might not want a 38-year-old running back on the team. It’s tough because I don’t know about next year.”

If the words of Gore’s teammates, ones that have more of an assured future within the organization, have been any indication, they’d be more than happy to have Gore back for another go at it.

“I respect the guy so much,” rookie and fellow rusher La’Mical Perine said of Gore, per Jack Bell of New York Jets.com in October. “We come in every week and meet one-on-one to go over the plays, every Wednesday. He’s a guy I look up to. I’m trying to find my routine, and he has a good routine. I just hope I can last as long as he has. He’s a great leader on and off the field. I just try to learn from him.”

“Frank has been an unbelievable veteran to have on this team,” general manager Joe Douglas said during an address last month, per notes from the Jets. “The leadership that he brings on a daily basis, how vested he is to help not only the offense but the entire team and especially young guys.”

Both rushing members of the Gore family will be back in action next weekend. The younger Gore will represent USM against UAB on Friday afternoon (12:30 p.m. ET, CBSSN) while his father and the Jets take on the Miami Dolphins at MetLife Stadium on Sunday (1 p.m. ET, CBS).

Geoff Magliocchetti is on Twitter @GeoffJMags