DesktopSearchField and Tab in it

I have a search window and have the use of the Tab key when I search stuff from adjacent Columns in a ListBox…

For some reason, I was not able to achieve that.

And… what if I want to go to the Results list (DesktopListBox with the keyboard (if I want to also be able to do that) ?

Xojo 2025r1.1
Sequoia
MBP 13" m1