Wiz,
Out of interest, what does your manual state as SOP for a T/A?
Everyone I have read says "Attempt to aquire tartget visually and maneouve as required".
You obviously don't fly Boeing 737s because the FCTM says:
Maneuvers based solely on a TA may result in reduced separation and are not recommended.
As for your scenario, have a read of event 4 in this document:
http://www.arinc.com/downloads/tcas/...our%20JULY.pdf
That could well happen to you when the other pilots spot you and do a similar dodgem manoeuvre.
As for correctly giving way to another aircraft at 900kts closure and with only a few seconds to visually acquire the other aircraft, "your ego's writing cheques your body can't cash".