Carl, I'm not convinced this is correct.
Both forward tip and aft tip have positive castor "trail" --wheel contact patch behind steering axis creates a restoring moment when yawed.
In addition to the amount of trail, there is also the effect of potential energy.
With the top of the axis tipped forward, the weight wants to make the wheel point straight aft. Any yaw deflection lifts the tail higher, so there is additional restoring moment trying to straighten the tail.
With the top of the axis tipped aft, the weight wants to make the wheel turn. It is happiest when turned 180 degrees, because that is the lowest height. So this vertical displacement effect is de-stabilizing.
I think Van got it about right - a slight amount of forward tip so the weight effect augments the castor effect.
It has been a long time since I studied castor shimmy, so this might not be correct, but I think shimmy occurs when the natural frequency of the yaw oscillation 'spring' from castor coincides with the natural frequency of the yaw oacillation 'spring' from vertical displacement. They feed each other like a flutter mode.
"The Magic Carpet" Flying since Sept. 2009
LS6-15/18W sailplane SOLD
bought my old LS6-A back!!
VAF donation Dec 2020