What do you mean that you have 'enabled global search'?

It is an option in settings

Global Search and Index (which I think is what you mean) is 'enabled' by default. Do you not have the search window at the top of the TB main interface? Or the search window when clicking on 'Quick Filter' (Ctrl+Shift+K)?

I read recently that Global Search is no longer enabled by default. I recently installed TB on a new computer and can confirm this. I changed it. I do not have the search window. I can produce the Quick Filter window with Ctrl-Shift-K but if I ask it to find 'drawings' it also finds 'draw', 'draws' and drawing and also gives incorrect locations for the emails it finds. I cannot restrict the search to a single account

Sorry for delay in reply but I was waiting until I could attach second monitor to my laptop

...if I ask it to find 'drawings' it also finds 'draw', 'draws' and drawing...

That has already been noted with words such as 'availability' and 'suitability'. It appears that a search term searches for all words that are connected to it and spelled similarly.

It may help rebuilding the database after compacting the folders - https://support.mozilla.org/en-US/kb/rebuilding-global-database

I do not have the search window - how do I get it?

I can carry out localized searches with Ctr-Shift-F except on those with .gmx addresses. Why is this?

I do not have the search window - how do I get it?

It's enabled by default. It should be at the top of the main user interface. The keyboard command Ctrl+K should bring it up or highlight it if it's there. You can reinstall it by using the Customisation options in View/Toolbars/Customise. Drag the 'Search' button to the middle of the arrows at the top

I'm a little concerned that you are running version 128.6.9 as we haven't got that far.

I can't help you with the .gmx query.