Identifying cause of light flickering?
It was a bad switch.  

The isolating it to when both switches were in the same position was as far as we could get for diagnostics.  All connections were inspected and seemed fine.  I finally gave in and just bought 2 new switches.  Upon trying to install them I noticed mismatches in wiring colors so I brought in an electrician who was able to sort things out (and tagged the wiring for me).  He then removed the oldest looking of the 2 switches and replaced it with one of my new switches.  The flickering problem is gone and I have a spare switch now...