Those traits contributed to fraud charges brought against Musk on Thursday by federal regulators, a potentially serious blow coming just as Tesla is ramping up efforts to become a mainstream manufacturer.
But on Saturday, the brilliant billionaire escaped the worst after reaching a settlement with the US Securities and Exchange Commission that leaves him as chief executive while forcing him to step down as chairman and pay a $20 million (roughly Rs . 145 crores) fine.
The settlement, which will leave the 47-year-old overseeing Tesla's daily operations, provides at least a momentary reprieve from the company's many challenges - including Musk's own sometimes counterproductive instincts.
Tesla is at something of a turning point. It has been accelerating production of its Model 3, the mass-market vehicle with a potential to disrupt the entire automotive sector - yet the company remains burdened by billions in debt and has yet to show a profit.
The SEC filing on Thursday alleged that Musk committed securities fraud by misleading investors when he tweeted on August 7 that he had "funding secured" to privatise the electric automaker at $420 a share, a comment that caused Tesla's share price to briefly spike.
The case underscored doubts about the mercurial entrepreneur's ability to lead Tesla, while at the same time highlighting the confidence some retain in him as a necessary visionary force behind the company.
"Despite Musk's recent erratic behaviour, we think most investors want him to remain with the company and they value shares at what we view as extremely lofty multiples given the potential for Musk's vision to drive future growth," Garrett Nelson of the research firm CFRA said in a note to clients.
Analyst David Whiston at Morningstar reiterated his comments from a month earlier that "Musk is effectively Tesla, and without him Tesla is just a capital-intensive automaker burning cash with too much debt due soon."
Tesla shares have skidded nearly 30 percent from their peak in early August, amid growing concerns on the company's ability to expand without its founder.
Criminal case coming?
Tesla's brash leader has faced increased scrutiny over his volatile behaviour, including smoking marijuana during a podcast interview and assailing a man involved in the Thailand cave rescue as a "pedo guy."
Musk initially rejected the SEC's allegations on Thursday, calling the charges baseless and vowing to defend himself. But investor pressure amid the tanking share prices may have given him second thoughts.
Tesla has continued to express support for Musk, saying the company and its directors "are fully confident in Elon, his integrity, and his leadership."
The SEC settlement may not end Musk's regulatory troubles, however, since there are reports of a pending criminal investigation as well.
Keri Axel, a former federal prosecutor and SEC enforcement lawyer who now is in private practice, said the swift filing of charges - so soon after Musk's August comments - raised eyebrows in the legal community.
"The timing of this is so fast, that seems very aggressive," Axel told AFP.
"One possibility is that the SEC is cooperating with criminal authorities" preparing to file additional charges.
But a criminal case would be much harder to prove since prosecutors would need to show "an intent to deceive investors," according to Axel.
'Everyone was wrong'
Gene Munster and Doug Clinton of Loup Ventures said in a research note that they believe Tesla will survive.
The sharp decline in Tesla shares is "an overreaction," the analysts wrote.
They had predicted, before the settlement was announced, that Musk could remain CEO and "find a way to continue to be involved with the company in some sort of product/visionary capacity."
They added that Tesla appears to have built up a sustainable production pace and that "the trajectory of the business is improving at a level that can support servicing its upcoming debt obligations and eventually generate cash."
Trip Chowdhry of Global Equities Research, a longtime Tesla bull, said his view on the company is unchanged by the SEC action.
Chowdhry said Tesla is "hyper-innovative" and that the company is essentially "in autonomous mode" in its production scheme, far ahead of rivals in battery technology.
"They are creating a brand new industry which never existed before," the analyst said. "It's software-driven transportation."
Chowdhry said that Tesla - with or without Musk - has a bright future because of its pace of innovation, and he compared Musk to the late Steve Jobs.