Fast blinking red light, but not battery/charging problem

My Galaxy Note 3 (SM-N900A with Android 5.0) has acquired a fast blinking red light (4 times/second) when the screen is dark. Everything else seems fine. The battery still holds a charge and charges as it always has. It happens whether the phone is plugged in for charging or not. I've rebooted, I've pulled the battery out and put it back in. I've gone to Settings -> Device -> LED indicator and unchecked all the boxes. Nothing affects it when the phone is turned on and the screen is off (due to timing out or me forcing it to "time out" by pressing the power button quickly).

I haven't found any documentation on what this might be other than due to battery problems, which I don't seem to be having. The phone is 3 years old and has spent almost all of its life plugged in for charging.

Any ideas what this means? Presumably it is a hardware notification, since it is unaffected by soft-disabling the LED indicator (on the one settings screen I mention above).