Furthest Station is a novella rather than a main novel, and provides all of the references to Rose Jars that I'm aware of prior to False Value.
Furthest Station's story centres around a series of Ghosts trying to alert someone or anyone to a 'captured princess'. The reveal at end shows these ghosts are captured within Rose Jars, but don't get much more exposition during the investigation than;
He was said to have married a creole lady from New Orleans and she knew how to make this thing called a rose jar. Which you're supposed to be able to catch a ghost in.
And then we end with;
Harold Postmartin, our archivist, promised to see if he could dig out any additional references to the jars or to catching ghosts in general from the semi-secret stacks at the Bodleian.
As far as I can tell Body Work never references Rose Jars directly. The story deals with hauntings of vehicles, but the mechanics of the possession are not part of the story which focuses on saving people and understanding the possession narratively rather than mechanically.