Pretty simple, but it’s been helpful. I added a big screw eye to a piece of scrap wood and attached it to the end of my lathe (using holes that were already there for attaching extensions etc). I put it on the headstock end because otherwise the hose was just underfoot too much.
This is my turning tool rack. Some PVC pipe screwed to a board, attached to the wall over a narrow shelf. The important bit (as I discovered with a previous attempt) is the gap between the bottom of the PVC pipes and the shelf, to let out any chips that get in the pipes.
The “business end” of the tool is up and exposed so I can find the tool I’m looking for. The rack is mounted high enough that I’m not going to accidentially stab myself reaching for a tool.