Earlier this year I had two vacancies. One resident contacted me to express an interest. She had 10 residents ready to sign a petition but asked me whether this was the best way to proceed. I advised her that interest in the vacancies was low, that an election would cost the council several thousand pounds and that it would not increase her chance of being a successful candidate. We have a formal process that selects the best candidate for the role against defined criteria specific to the vacancy and it was clear to me that she would be selected in a competitive co-option process if the unimaginable happened and we had more candidates than vacancies (although I didn't tell her this as it's not my place to do so). No election was called, she was duly co-opted and the council saved itself a sizeable chunk of money that has since been spent on improvements to the children's play equipment.
My only previous experience of a petition occurred a couple of years ago when 10 residents submitted their petition on the grounds that it was good for democracy, then didn't put forward a candidate, so no election was held. Once the election had been called, the vacancy could only be filled by election, so a second election was called and a candidate with no connection to the petitioners threw his hat into the ring and was duly elected as the sole candidate, with no election and a saving of over £4k for the council.
I am fortunate that two of my three parishes have regular newsletters that are distributed to every household, so it's relatively easy to keep residents up to date with matters such as vacancies and elections. Apart from our own website, we also use noticeboards and Facebook. We seek to educate our residents regarding their powers in such matters.