it seems like you forgot an IMPORTANT THING
pls review your manual at page 73 and page 77
61 point automatic selection AF both in A+ and AI Servo Modes
dont worry, there's nothing wrong with your 5D3, just wrong user settings.
we all experience it - one way or the other.
Wife says we can't afford a new user, so its up to me still.
My manual is in German so not totally certain what points you are referring to as the page numbers may be different.
I watched all three videos and read the book (EOS_5D_Mark_III_AF_setting_guidebook.pdf) again. With AI Servo AF with all 61 points used, it says "Shooting started by pinpointing focus on the leader of a cycling road race with a manually selected AF point". I'm still unclear on the "manually selected AF point", the large picture on page 53 shows 61 points in use.
Just testing getting the camera to focus on a stationary object indoors, it will do that with one of the outer points. Selecting the point or points it uses on its own.
When shooting BIF, usually pretty small ones in our garden, I find I need to anticipate a lot in which direction they will move, for example when taking off. So I will try to track them as much as possible, but I'm hoping for some assistance from the 61 points to get/keep the bird sharp as long as its under an AF point.
Anyway thanks to everyone for the help and patience.