IO540:
I have an STec 20 and a GNS430. Your post has prompted me to start by reading the manuals to see how the STec gets its signals when following either the GPS or VOR in NAV mode. I assumed the autopilot got a 'track-error' signal from the GPS/VOR and the computer in the TC generated the turn command. As you suggest, it's better to know BEFORE things start going wrong. Although it's manatory to carry the manuals, you really can't read them when you suffer gyro failure in IMC!! ;-) I'll post more in a few days.
Purely personally, I agree that a practical reality is to use GPS as primary guidance and confirm that all is well using map or conventional nav instruments. This is what I do and this is the way I was advised to do NDB and VOR non-precision approaches by my IRE -- using an IFR approved GPS with a current database, I hasten to add.
Style:
I have not used the Garmin 196 (Is this the new one with visual screen representations of instruments?). Do you get a rapid screen response to changes in aircraft attitude and performance? Is it sufficient to use if the gyros fail, or are you better to use conventional techniques?
I have checked my GPS altitude readout and found it typically agrees with the altimeter within 50 feet when I have a good satellite constellation (I have an external aerial). There is also good agreement at typical IFR rates of descent, around 500fpm. The GPS keeps up well. Hence my preparedness to use GPS if I lost the pitot/static.
So far as using GPS groundspeed is concerned, remember if you lose your pitot/static in IMC, the back-up is to use "Power + Attitude = Performance." This is pretty imprecise. If you have been flying for a while before pitot/static failure occurs, you will have a good idea of the wind and of the difference between groundspeed and indicated airspeed. You use this to help you derive airspeed from GPS groundspeed. This helps to confirm that you have selected the correct attitude and power to get the performance you want.
In my long-winded way, I am trying to say that if you lose your gyros or your pitot/static then use all the remaining tools at your disposal!
AA.