It belongs to the Item, not the link, and it’s really constructed from a bit here and a bit there, so you won’t find it by inspecting JSONDB
Use API Explorer to view the Items, it pulls this together in JSON form.
To give this thread an end:
For unknown reasons, after updating to 3.4.0, switching completely to .things/.items and fixing a ton of errors/mistakes I made in the first place with my items, it now works. Dunno why, but who cares - it does work 
Another issue now is that this distinct item does not show up in my thermostat popups, but that’s worth a different thread if I cannot get around it.