Most of these types of cars were listed as "Water cars" The railroad was obviously using 09410 for water as well as coal as displayed by the work to the spicket at the front left side of the tender tank.
From Steve Swanson's great presentation on water cars:
"In 1924, three ex tenders were renumbered as water cars W480, W481 and W482. It is the thought that these three cars were intended for water and coal service in extra gang and B&B outfits.
In 1926 , fourteen ex tenders were retained from twenty-nine C-16’s and five T-12’s being scrapped and were numbered W483 to W497.
Again in 1934-7, fifteen C-16’s and five T-12’s were being scrapped and five tenders from these engines became W class water cars. Four replaced existing water cars: the tender from engine 206 became second W481 as the original tender was scrapped, second W484 came from C-16 #214, second W488 came from C-16 #265 and second W492 came from T-12 #174. C-16 #218’s tender became W498.
As these ex tenders were retained from engines being scrapped and it is presumed that they were the tenders in the better condition, still these cars probably needed more attention than was justified and with the continuing retirement of older small locomotives, there was a source of replacements."
Later as the wooden frames on the tenders were worn out, tanks (cisterns) were placed on flats instead of rebuilding the frames such as 06204, 09410 and 06209. They all lost their numbers in preference to the flat car number. The series was started before the K-36s and K-37s but I would think the 36s were ordered and the railroad would have already assigned them numbers. I further guess that, like the 40' reefers, since the tenders were now rolling stock they could be numered the same as locomotives. Then just to "narrow gauge funk" it up a bit, W-462 and X-347 had different prefixes and retained their loco numbers.