Electronic – Intuitive and iterative approach to understanding of blinking LED circuit

This circuit is called an astable multivibrator, and the reason this circuit works is a little difficult to put into words.

Take a look at this circuit simulation that shows visually what is happening. You can slow the speed right down and look carefully at how the current is flowing.

While one of the capacitors is charging, current flows to the base of the alternate transistor, making the emitter-collector path conduct, making one of the LEDs light. When the capacitor is charged, it stops conducting and switches off the transistor, and then the other capacitor begins to charge switching on the other transistor, at the same time the first capacitor discharges, then the cycle repeats.

I didn't read your whole question, which seemed to go out of its way to make a simple thing complicated. As I understand it, you have a capacitor, resistor, and LED all in series, and you want to know how things decay if the capacitor starts out initially charged up.

At first apporoximation, you can consider the LED a voltage source. That means the current will decay just as if the LED wasn't there and the cap was charged up to the LED voltage less than what it really was. This is now a simple R-C systems which follows a basic exponential decay with a time constant of RC, which it seems you already understand. The question of when the LED goes "off" then comes down to at what current you consider the brightness to be low enough to be off. This can vary a lot by the efficiency of the LED, ambient light level, and how obvious "on" is supposed to be. For example, if the cap is initially charged so that the initial current is 20 mA (a common maximum for LEDs) and you consider 1 mA the "off" level, then the on time will be the 95% decay time, which is 3.0 time constants.

As I said, this was the basic first approximation where the LED has a fixed voltage accross it. That will be largely true, but of course its voltage will drop with current somewhat. For practicle purposes, this is a small effect compared to the slop of deciding what current level "off" really is, unless that current is small, like less than a mA.