Update: A/C working
Below Ive made a short video to show the entering into the diagnostic mode on the climate control interface.
Basically you push and hold the up and down arrow buttons for a few seconds until the display reads 00.
Then you use the up and down arrows to cycle through the different data modes, and the AUTO button to read the value of the data stored in each state register.
When you want to get out of the diagnostics mode, you hit any of the other buttons, I think I used the OFF button.
When I took my vette to my trusted mechanic, he looked at the problem and found no power to the A/C components and thought there were more things wrong than just the low freon level that I said the diagnostics mode indicated (00 state, 09 value = low freon). I remembered reading here that the battery power needs to be disconnect to reset the system once the blinking LEDs happen. So when we pulled the power and reconnected, the power was restored to the A/C systems so we could then continue our A/C component checks. Apparently the A/C system gets shut down when theres a problem, and the blinking LED is an indication of such. Until we toggled the battery power (not just the ignition switch with battery attached), we couldn't get the system running even after recharging the freon (which is about 60 bucks per pound of pressure, if you can find it at all and most shops don't have the system for removing the old freon any more). Once we recharged the freon, and cycled the power off the battery; the LEDs stopped blinking and the 00 State is back to 00 value (healthy).
One last note which was learning for me...
The spec for a working A/C system for these older cars is that it should be able reduce the ambient temperature by at least 30 degrees at its max cooling settings. This was measured by putting a turkey thermometer into the A/C vent. And sure enough, it was 90 ambient and we got down to 60 degrees. Mission complete. I should take the car back after a week or so and have them use a sniffer to see if there are any leaks.