"Hidden" products on 7.1 site - behavior & listing

Site URL: https://www.thebluehousebethesda.com/

I've got a client who keeps flagging various products in their inventory as "hidden", but checking the live site sometimes shows the product is still visible on product pages as well as search results. I'm using a 7.1 template, and I'm curious as to the parameters for this function. Does hiding a product happen instantaneously, or is it more of a "24 hours later" thing? My testing leans towards the latter. Does anyone else have any input on this?

Additionally, is there a way to display or search for items in inventory that have been flagged as hidden? As it is now, all I can see is either manual browsing to look for the tag in the inventory list, or exporting the inventory as a spreadsheet that I cross-reference with the site.