Grouped checkbuttons in a popover aren't accessible

I have three grouped checkbuttons (thus, three coupled “radiobuttons”) inside a Gtk.Popover, and use toggled signal to close the popover when the user chooses one with the mouse. The problem I have is that, when using the popover with the keyboard, the only way of navigating the checkbuttons is using the cursor keys (TAB does nothing). But moving the focus from one checkbutton to another with the cursor does trigger the toggled signal, so the popover is closed.

So the question is: how can I make the grouped checkbuttons navigable using the keyboard, and only toggle one when pressing Return or Space (thus, “activate” signal), but, at the same time, close the popover when the user selects with the mouse any of the checkbuttons?