There also is the magic speed at which countersteering starts.Without searching, seems around 23mph was the consensus. What works at parking lot speed will not work above that threshold and vice versa
This is NOT really true. I would refer you back to Newton's principle of motion. That things in motion will stay in motion until acted upon by another force. This happens at 2 mph as well as at 60 mph.
I would suggest to you simply that you think that it is different but it is not. If you identify the C/G of the mass of the bike, and then (even at slow speeds) it will "want" to continue in a straight line unless acted upon by another force. Steering to the right or left, the mass (c/g) wants still to go straight - and it does - forcing the "fall" as gravity has more and more influence. Since it is going so slow (at 2 mph) it seems that there is something different going on than at 60 mph, but not so. Newton's principle is still in effect.
What I suggest is that since it is such a slow speed, it takes very little force to counteract Newton's straight line principle that it is difficult for the rider to apply that little of force with consistency - resulting in the seemingly wobble at the slow speeds. Why there is not a "consensus" as to when countersteering starts is due to the various riders' abilities to "control" the bike - some riders are better at it than others
If you watched the video that I posted from YouTube it explains that the phenomena of countersteering works on a motorcycle/bicycle at both slow speeds and at high speeds.
Try taking out a bicycle and slow speeds, and you will be able to detect the countersteering principles working when you are just going 3 or 4 mph. You don't need to get up to 20 mph to have it start to take affect.