KUALA LUMPUR, Malaysia—On a recent humid afternoon, experts holding forth here on why former Malaysian Prime Minister Mahathir Mohamad was too old to fight another campaign were stunned into silence when the 92-year-old walked in, took a microphone and said, “As far as health is concerned, I’m not senile yet.”

Many in the audience cheered the unlikely leader of the opposition, now on a mission to vanquish Prime Minister Najib Razak, the current leader of the party Dr. Mahathir helmed for 22 years, in elections May 9. Dr....