Some Apple II motherboards have a red LED in the back-right corner near the joystick / cassette in/out connectors. I have never seen it illuminated. What is its purpose?
This is the self-test LED. Here's a quote from Sather's excellent Understanding the Apple IIe.
There is an LED (Light Emitting Diode) connected across the speaker jack on the Apple IIe motherboard. However, the LED (CR2) does not normally light because there is not enough voltage developed across the speaker primary to cause visible light emission. The light does glow when SPKR is toggling with the speaker disconnected. You can see this for yourself by disconnecting the speaker plug and holding open Apple and close Apple and pressing CONTROL-RESET. This causes firmware diagnostic execution with speaker tones or light emission from the LED when the speaker is disconnected. The LED thus provides a means of verifying diagnostic performance on a motherboard with no speaker connected.