Just a comment here from my own experience.
I have never experienced a gyro failure for real but have experienced it multiple times in the sim. The first time I did what the first post indicated in those accident reports - ended up in a steep descending turn that would probably would have ended badly if for real
So WHY - WHAT happened
A couple of things - gyros can spin down slowly causing erratic, unpredictable or even insidious behaviour that in my case indicated a very slow increasing turn to the left which i blindly followed maybe over several minutes as it slowly spun down - by the time I realised I had almost lost control
And by the way I had already practiced and was reasonably competent at flying on partial panel with the instrument covers on in the aircraft
So what did I learn
(1) importance of a comprehensive scan - they only way to detect a failure is to use supporting instruments to detect and verify a failure
(2) the AH is evil when it dies - it can be initially undetectable - be wary !!
(3) while it is good to practice partial panel in the aircraft - its actually not to difficult when the instructor has just told you the instrument has failed and covered it up - you know whats happening and adjust your scan - much, much more difficult and realistic in the sim with a "real" simulated failure
(4) last point - always carry a few instrument covers or post notes that can be used to cover up failed instruments as it can be distracting - in my case I had a TC fail in IMC - not a problem but distracting