Lazarus bug in linux qt5 & win32. gtk2 version is ok.
IDE shows that even 1st click calls MouseDown which calls SetFocus. but 1st click does not call DoEnter method of ATSynEdit! so ATSynedit does not set flag FIsEntered and this disables the caret blinking.
2nd click - calls DoEnter and then caret blink is enabled (FIsEntered=true) and caret begins to blink.