There several sites that say Jackie Gleason did own a private car.
Terry Bebout, who has been president of the Tennessee Central Railway Museum in Nashville since 1985, has always loved trains. Bebout grew up near Tennessee Central Railroad and has long enjoyed building model trains. When he was little his grandmother took him on a train, and he told her that when he grew up he would own one. He now owns his own private coach. Bebout said a lot of work goes into fixing up the trains. Tile, carpet and windows are replaced. Seats sometimes must be reupholstered and walls repainted. Mechanics, plumbers and other specialists come in and voluntarily work on the trains.
Some of the cars and coaches are privately owned. Bebout's coach previously belonged to entertainer Jackie Gleason. It has a lounge, bedroom, bathroom, dining room, kitchen, and crew
quarters. Gleason used to ride his coach from New York to Boston because he was afraid to fly.
The Tennessee Central Railway Museum is also the Nashville Chapter of the NRHS. And from the museum's newsletter:
TCRX 103 has an interesting history. It was built by Budd in 1950 as SP 9012, a 10-6 sleeper. SP sold it to the Pickens Railroad in South Carolina where it was converted into a stainless steel business car named Edna III. The Pickens Railroad sold the car to comedian Jackie Gleason who typically used it on trips between New York and Florida. The car briefly was owned, but never used, by Auto Train Corporation. After Auto Train released it, it was stored in Florida for several years.