my two cents worth at attmepting to clarify:
-all the gyroscopic forces etc are all there, but basically when you countersteer right, for an instant the front wheel runs right, just like a car. However, then the tire contact patch is out from under the cg. Since the driving force is outside of the cg, the bike will now turn left. If you have ever driven a skid steer loader, driving the outside wheel turns the machine around its cg. The bar pressure initiates the turn, then the corrections keep it in balance.
-dirt track bikes and cars initiate a turn in, but use throttle steering of the rear wheels, which is a whole different topic.
-in the air, the rear wheel is a great flywheel. throttle reacts against it, essentially doing a wheelie up. Rear brake couples the bike to the rear wheel momentum and tries to rotate the bike in the direction of the wheel, i.e. down.
-tire profile: I had a wider shoulder rear tire on a bmw that did not match the rounded front profile. As the bike leaned over, the front contact patch moves a certain distance, fairly small distance. However, the back contact patch moved way inside because of the flat sholder. imagine leaning over on a 10 inch wide roller. the contact patch would now be the inside edge, 5 inches inside of c/l of bike. In my case, it usually tended to drive the rear outward at a more unpredictable, faster rate. Sort of an oversteer effect. Unpredictable, I didn't like it. My own fault, as the profiles were not a matched set, so I changed it.
kcj
observed trials rider, (barely)
mc rider for 35 years
engineer