The Mini, number plate MF55 YHM, is said to be “key to establishing her whereabouts”.
A friend who was the last person to see missing mother-of-two Alexandra before she vanished fears something may have happened to her.
Petrol station manager Rose McAuley, 32, served the 34-year-old when she topped her Mini Cooper up with £10 of fuel and bought a coffee and snack.
The mother-of-two also laughed with her friend of 17 years, who she first met at a local youth club, after tripping over a wet floor warning sign.
Mother of two Ms Morgan, known as Alex by friends, has not been seen for 10 days since making the purchases at 7.20am on November 14 – Remembrance Sunday.
Her white Mini Cooper was spotted making journeys between her home in Sissinghurst, Kent and towards the Hastings area of East Sussex on the Sunday she was last seen and the following day, Monday November 15.
Ms McAuley, who also lives in the village near the Sussex border and has worked at the garage for nine years, said: “I don’t think anybody knows what’s happened to her or where she’s gone. For her car not to be seen at all since then is a complete mystery.
“A friend and I went around Hastings looking for it but didn’t find anything.
“Alex never gets embarrassed so I don’t think it’s a case of her being afraid to come home. I just hope nothing bad has happened to her.
“I just hope she’s okay and turns up. It’s really worrying.”
Ms Morgan, who Ms McAuley says used to run a dog grooming business, said she was planning to visit friends in Yorkshire for a week but complained her black roofed Mini needed repairing.
Ms McAuley said of their interaction: “Alex often comes in without any make up on and in comfy clothes as this is her local shop, as you would.
“But she was really dolled up with a full face of make up, her hair done and wearing nice clothes when she came in that Sunday looking very well presented.
“She was more done up than I’ve ever seen her before. And she came in very early in the morning which was unlike her. She put £10 of fuel in and bought a coffee and a snack.
“Alex seemed in a good mood and was smiling. She was just your usual Alex – tripping over the wet floor sign and laughing about it.”
Police have taken CCTV from the garage and interviewed Ms McAuley for a description of what Ms Morgan was wearing and how she behaved when she was last seen.
Detectives from the Kent and Essex Serious Crime Directorate are leading the investigation.