"Out of stock" without counting inventory

Hi all,
I imagine this is a simple fix, but I haven't been able to find the place to do it or the proper search terms to find the answer.

I do not wish to use the inventory counting feature. When an item is out of stock, I'd like to tag it as such so that it is visible but customers can't order it. It seems like I should be able to use the "out of stock" radio button for that, but that removes the item entirely. I want it to remain visible but show the out of stock icon and not allow it to be added to the cart.

I am using Zen Cart 1.3.8. The site is https://www.interlitfoundation.org/shop. Thanks in advance for your help!
Best,
Leah

If anyone knows how to do this I would be interested too.

In Admin - Configuration - Stock, there's a 'Product Status in Catalog' setting that might do what you want.