Tesla Inc.'s plunging stock price indicates investors want Elon Musk to quickly cut a deal with the Securities and Exchange Commission. The question is whether the notoriously unpredictable chief executive officer will take the hint.

In suing Musk on Thursday, the SEC put shareholders' worst-case scenario on the table: Musk's potential ouster from Tesla. The regulator had offered a much lighter punishment that would have allowed him to stay on as CEO while paying between $5 million and $10 million, according to a person with knowledge of the matter. Tesla would have also faced a financial penalty, though lower than Musk's.

But the accord was refused, and Tesla shares have tanked. That puts intense pressure on Musk and the electric-car maker's board to stop the bleeding.