Joe Lonsdale, a tech investor close to Mr. Musk, is not planning to play a formal role in the Trump transition, according to a person briefed on the matter, and he has said publicly that he does not want to join the administration “full time” but would rather play a part-time advisory role.

Musk has been so aggressive in pushing his views about Trump’s second term that he’s stepping on the toes of Trump’s transition team and may be overstaying his welcome at Mar-a-Lago, Trump’s home in Palm Beach, Florida, according to two people familiar with the transition who have spent time at the resort over the past week.