Yes, the coach was a little un-cared for, it had stood at Old Dalby for 5 years, then after transfer to GCR it stood at Rothley for another 2 (as seen here in 2018),
https://www.flickr.com/photos/82085846@N02/48654471588
There's a lot more pics of the coach during it's life in my Flickr album,
https://www.flickr.com/photos/82085846@N02/albums/72157705726190461
As for other test coaches, in BR days these were split between the DM&EE (which were'Test Cars') and the BR Research department (which were 'Laboratory Coaches'). Of the DM&EE coaches there are a few in preservation including Test Car 1 which is at the South Devon railway but returned to passenger use, Test Car 2 at GCR, and the original Test Car 5 which ended up in the Crewe Works test train, I believe is at Peak Rail. Test Car 3 (Mentor) is still in the Network Rail fleet and Test Car 10 is still in use in the NMT. There are also a few laboratory coaches preserved including Iris at Wirksworth, Lab 11 at Dartmoor and the Trib train auto trailer I think was at WSR.
I think Test Car 2 is unique in preservation being the only test coach preserved as a test coach !