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Jim Beam writes:

Take the wheel out, spin it in you hands and try to tilt it to the
left or right and note the force of the steering action. This
should convince you of its effect.

please explain. gyro reaction is _90 degrees to the applied force_.
i.e. my front wheel, spinning "forwards" tries to tilt top
rightwards when turned to the left. you seem to be implying that
gyro recation is responsible for banking the bike to the left when
steered left.

Not at all. I suggest that the wheel spinning forward steers to the
left when tilted to the left and to the right when tilted to the
right.

I wouldn't disagree with the above.

This is the means by which the bicycle steers when walking the
bike while held by the saddle and also what enables it to be ridden
no-hands.

What is the relative contribution of the different effects - ie to what
degree is the above more important than the effects of rake and trail - at
different speeds and with the addition of the rider to the whole system.