Ms Timms was not answering calls at her Lumsden home or on her cellphone.
Asked if he thought Cr Timms should resign, Mr Shadbolt said that was not for him or his council to decide.
However, he said it was "probably an option Cr Timms would think about during her leave of absence".
Her hoax call could not have come at a worse time, he said, referring to the Australian radio DJs' call to a London hospital posing as members of the royal family which resulted in the death of a nurse.
"If [Cr Timms'] call had been on April 1, then that might have been all right.
"But the Australian-English situation has probably magnified it. This is just not a time for making joke calls."
During a conversation lasting almost 10 minutes "Ruby" quizzed Mr Shadbolt on the talkback show about the community benefits of the planned Auckland to Bluff yacht race and who would pay for the race expenses, including the infrastructure needed to moor up to 30 super and maxi yachts at Bluff.
About eight minutes into the conversation Mr Shadbolt called her Ali, to which she replied: "Sorry, who? This is Ruby here".
Mr Shadbolt said he was "very suspicious" from the start that Ruby was Cr Timms but did not want to denounce her on air in case he was wrong.
"I threw in Ali twice to give her an escape, but she was quite adamant she was Ruby. If she had said 'fair enough, it's me', that would have been a joke, but she didn't."
He said Cr Timms rang him and apologised but did not view it as a prank.