I dont have an Omega to check any more, but from memory:
A/C off (or A/C broken)
Front 2 fans are off, coming on slow speed when 1st temp switch hit (around 92C?), high speed when 2nd temp switch (97C?).
Slow speed fans will continue after ign switched off if 1st temp switch still activated.
A/C on (and functional)
Rearward fan on and front 2 on slow speed, front 2 high speed if 2nd temp reached
Front 2 slow speed stay on with ign off, if 1st temp switch activated
(Temps are the switch value, bear no relation to the dash, but should correlate-ish to ECU coolant temp sensor). On V6, I seem to recall both temp switches are in the same screw-in module in the rad)
Can a v6 owner confirm my memory?
From this, further testing can be done by shorting out temp swicthes with a paperclip and a/c off, checking what happens.