"Tabs" (Menu Local Tasks) are a strange UX drupalism (soon to be a backdropism too). Before we had contextual links, tabs made some sort of sense: we needed a way for people to edit things directly from where they are viewing them.
But now we have contextual links, these links allow people to edit all kinds of things directly from where they are viewing them! Let's move the links that are currently displayed as "tabs" into contextual links instead, and see if we can get rid of this concept of Menu Local Tasks.
We have a lot of administrative listings that are currently being displayed as tabs, for convenience. These items would need to be converted into MENU_NORMAL_ITEMS instead. ( IMO, that's what they should have been in the first place, so this will be just a return to normalcy.)
Recent comments
I'll test this tomorrow to see if I can replicate the problem and report back. It's not "per user" so it should be working.
TFA - how to setup fallback options 'per user'
As I work through things I flush the caches after every change I make. As far as I can tell I have the custom module in the correct place (/modules/custom/fix_zero_search) and the file...
custom module not showing up in modules list
If you haven't already, flush all the caches. If it is in the modules folder whether directly or in a custom folder it will show up. If not, something else is wrong with your site; check...
custom module not showing up in modules list