Mr Gibson, from Woodhall Spa, was last seen in the village almost three weeks ago, at around 1.45pm on the afternoon of Thursday November 28.
His car, an Audi Q5, was parked at 3.15pm that day close to the Railway Inn, at Kirkstead Bridge.
Lincolnshire Police have today (Tuesday) released CCTV images of several dog walkers who may have spotted Mr Gibson on the day.
A police spokesman said: “Are you one of the people featured in these photographs?
“You may have information which could help us in the search for missing 82-year-old man Fred Gibson.
“The people in these CCTV photographs may have seen his vehicle, or Fred himself, on the day he was last seen, and may have crucial information which would help our search. We appreciate that the images are not the clearest, but we are publishing them in an effort to trace these people.”
Mr Gibson is described as white, 5ft 10ins tall, with short hair. He was wearing a blue top, jeans, and a sleeveless shooting jacket.
• If you have any information, call Lincolnshire Police on 101, quoting incident number 384 of November 28.