With Elon Musk's visibility 'there is incredible isolation,' leadership expert says

Shares of Tesla dropped sharply in after-hours trading Thursday court documents showed the Securities and Exchange Commission is suing Elon Musk for fraud.

Tesla (TSLA) CEO Elon Musk's feelings of exhaustion "are not uncommon for leaders" in his position who face growing pressure, leadership wellness expert Lowinn Kibbey told CNBC on Friday.

"I think what Musk has done is illuminate an issue that many leaders feel," Kibbey said on CNBC's "Closing Bell."

Following months of bizarre behavior from Musk, The New York Times published an extended interview with the Tesla CEO in which he said the past year has been "excruciating" and "the most difficult and painful" of his career. In the emotional interview, Musk revealed he has been working as much as 120 hours per week, which caused him to work through his birthday and almost miss his brother's wedding. The CEO also revealed that when he gets a rare moment of shut-eye, it is often with the help of sleep aid Ambien.

Shares of Tesla (TSLA) tumbled 8.9 percent Friday after the interview was published.

Kibbey is global head of the Johnson & Johnson Human Performance Institute, which runs a program that works with athletes, the military and Fortune 500 CEOs to train them for high-pressure roles. He said the nature of the CEO role, as well as other high-level executive roles, has become more stressful with the advent of social media.

"The CEO role is an incredibly, highly visible role. There is tremendous stress in it. And over the last, say, five years, that stress has grown even greater, with complete visibility — from social media, pressure from activist shareholders, short sellers," Kibbey said.

"With that visibility, though, there is incredible isolation. It is very difficult to share what's going on in a way where you feel people can have empathy and you can trust them," he added.

It's Musk's erratic behavior, both on social media and off, that has invited much of the recent criticism of his character and management style. Most recently, his tweet that he would take Tesla private at $420 per share and had "funding secured" has invited scrutiny from the Securities and Exchange Commission .

In July, he took to Twitter to call a British cave diver who assisted in the rescue of a Thai boys soccer team a "pedo guy." During Tesla's first-quarter earnings call in May, Musk dissed analysts, cutting off Sanford Bernstein's Toni Sacconaghi because of what he called a "boring, bonehead" question. Musk later apologized to Sacconaghi and to the diver, Vernon Unsworth, for his comments.

As executive roles change, companies should change their approaches to training those executives, Kibbey said.

"There has to be a whole-person approach to this. No one has talked about this before; it's always been about what results have you driven in Q3 or Q4," Kibbey said. "But the truth is, if that leader is not showing up physically well ... if the mental, emotional resilience is not there, if the character-driven leadership is not there, that creates risk."

The stakes may be high, but Kibbey said that doesn't mean Musk should step down as CEO and chairman. Instead, he applauded the entrepreneur for his transparency.

"This problem is common, and what Elon has done today is courageously talked about the pressure of that role."