The S3 light blinks out trouble codes for the automatic transmission. Here's what my Helms manual says:

The Transmission Control Module (TCM) has a built-in self-diagnosis function. The S3 indicator light in the gauge cluster assembly and LED indicator on the TCM blink when the TCM senses an abnormality in the input or output systems. The number of blinks from the LED indicator varies according to the problem, which can be diagnosed by counting the number of blinks.

When the ignition switch is turned ON, the S3 indicator light comes on for about two seconds regardless of whether there is a problem. The S3 light will also come on in S3 mode.

If there is a system problem, the S3 indicator light will come on and continue to blink until the ignition key is turned OFF. When the ignition key is turned ON again, the S3 light will not blink again for the original problem. But if the TCM senses the original abnormality again with the ignition switch ON, the S3 indicator light will blink again for the original problem. Therefore, even though the S3 indicator light does not come on when turning the ignition key ON, check the LED display for automatic transmission problem diagnosis."

I can post the section on troubleshooting the TCM if you like.