10:00 AM PT -- A source close to Elon tells TMZ, "Amber invited Elon to her favorite restaurant for lunch, which serves cuisine from her home town of Austin. They caught up and kissed goodbye, but are not back together."
Amber Heard and Elon Musk wasted no time re-igniting an old flame ... marking their territory with a kiss.
The actress and the genius behind Tesla and SpaceX grabbed lunch Thursday in L.A. and, just before hopping in separate cars, Elon reached behind Amber and planted a smacker.
The PDA-heavy lunch comes about a month after TMZ broke the story ... Amber and Elon were together for the first time since announcing their breakup in August.
The timing of that reunion was revealing ... one day after Rolling Stone posted an Elon profile in which he said how heartbroken he was about breaking up with Amber. He told the mag, "I was really in love, and it hurt bad."