I remember experiencing shimmy on the tailwheel of the 185 in my first days in PNG and my then CP explaining that the tw was actually doing 360s (rather than a high frequency wiggle) as we rolled down the runway...looking at the marks on the tyre this seemed a reasonable explanation...it certainly felt like that...my instant reaction was to push the stick forward an unload the wheel which worked.
What causes it?
Unbalanced wheel or tyre/uneven wear/not fitted 'square'/loose/not greased regularly etc...and/or a worn out shimmy damper for nosewheel aircraft.
I never experienced tw shimmy on grass that I can remember - seemed to only happen on sealed runways - one of the reasons I eschew 3 pointers on tarmac.
I remember having an ongoing battle of will with the other pilot (there were only ever two of us at Simbu Aviation) when I later became CP over how tight the tailwheel bolt should be on the 185 - He always loosened off the bolt to give easier ground manouvering - it came out of the steering range and into castor easier - this meant it was also more prone to shimmy. I always wanted it tighter which meant it took more effort to get the tw to castor but it never shimmied. We also had an ongoing good natured argument over who got to fly the 185 and who got to fly the Islander on any given day - we both loved to fly the 185.
Maybe he was prescient - he died in that Islander the following year.
I think, for tw aircraft, keep the system greased with fresh grease regularly, keep it slightly on the tight side of perfect with respect to how easy it castors (if there is a clutch that gives a steering/castoring range) and keep the weight off it as long as possible on tarmac.
Unloading the wheel if it shimmies is just basic airmanship. Certainly unrestrained shimmy does enormous damage over time and WILL lead to failed components - over the years in PNG I had several occasions where a brief shimmy caused the center bolt to fail completely and the whole ****fight departed the aircraft.
On a nosewheel aircraft you risk damage to the firewall where it mounts in fixed gear aircraft and, in retractable gear aircraft, you are hammering the extension/retraction system components which could easily lead to not being able to extend the nose gear one day...with all that entails.