The late actor's former home has just been listed for sale at $12,950,000 ... and it's got a pretty interesting history ... including some links to Elon Musk.

Gene bought the place way back in 1976 for about $300K ... making the big purchase after his 1974 movie "Young Frankenstein" became a hit.

The place has 4 bedrooms, 5 bathrooms and 2,750 square feet of living space ... plus a kidney-shaped pool in the backyard, overlooking the Bel-Air Country Club golf course.

Wilder lived there for decades, until he sold the property in 2007 for $2.75 million ... and in 2013, Musk snapped it up for $6.75 million.

Elon owned a bigger -- and newer -- house across the street at the time ... and Musk preserved Gene's eclectic home, using it as a place to host parties and events.

When Elon announced in 2020 he was selling all his physical possessions, he put the house on the market for $9.5 million ... and made it clear he wanted the next owner to keep the home as is, instead of knocking it down and starting fresh.

Ultimately, Elon made a deal with Gene's nephew, Jordan Walker-Pearlman, who had grown up in the house with his famous uncle. Elon sold the place back to the family for $7 million ... with the stipulation Jordan would not alter the home's "soul."

Elon lent Jordan and his wife, screenwriter Elizabeth Hunter, $6.7 million -- and in October 2020 the sale closed ... and Gene's home was saved.

Now, Gene's place is back up for sale ... hitting the market the same day the Wall Street Journal reports Jordan and Elizabeth have fallen behind on loan payments.

The WSJ also reports an entity tied to Musk recently filed a notice of default on the home ... an early step in the foreclosure process.

Elon can reportedly force a sale in the next few months ... and it appears Jordan and Elizabeth are going to try to sell the place before the deadline.

Our sources say Gene's family and Elon share the same wish here ... for the house to keep its original soul ... and we're told that will be part of the deal.