Broadcaster and radio historian Wayne Mac emailed to tell me the Bearded Beetle's name was Dave Dexter. He was the panel operator at 3DB who recorded a song called The Bearded Beetle with announcer Barry Ferber in 1964. No other details yet, except that Wayne believes Dave Dexter died in a car accident in New Zealand.
I did find a reprinted magazine article from the 70s about Radio Hauraki, the pirate station that became New Zealand's first commercial station, and there is a Dave Dexter amongst the station's disc jockeys. (Not to be confused, I should hardly need to add, with Dave Dexter the Capitol Records producer and executive.)