My solar light internals

I took apart one of my solar lights and found it contained a single AA sized battery and the following circuit board, which has 2 resistors, 1 electrolytic capacitor, 1 diode, and the LED, as well as the round black blob I labeled "?". The light operation is: cover the solar cell, the LED immediately lights up, cover it and the LED immediately turns off.

The round black blob has 5 traces running into it. I suspect there is some circuitry on the board, and the black stuff was just a drop of some liquid (when it was applied) sealer to protect it... I have drawn a rough schematic but I can't quite figure out what the "?" component is/does. Can anyone shed some light on this circuit for me? Also, the 1.2v doesn't seem to be enough to drop across the diode and the LED...

The black blob is a potting compound. It is intended to prevent you from finding out what is underneath it.

It is probably some sort of integrated circuit, but directly bonded to the board, rather than being in a separate package.

Many mass-produced items like calculators, tv remotes etc are built like that. https://www.empf.org/empfasis/dec04/improve1204.htm

I think that the diode - capacitor - led - ic arrangement is a charge pump to give more than 1.5 V to light the LED

for your reading enjoyment you may want to search under "jewel thief"

https://upload.wikimedia.org/wikipedia/en/f/f7/Return_of_Jewel_Thief.jpg this one?
... the BB code here doesn´t behave AT ALL like BB code should

I thought of a joule thief circuit, but all the ones I have seen have an inductor and there isn't one on the board that I could tell.

Of course the circuit uses an inductor (you show it as a 2k resistor) because it still lights the 3.3V LED when the battery voltage has dropped to 0.9V. The inductor looks like a resistor.
My solar garden lights that use an ordinary LED do not use a capacitor parallel with the LED. The solar garden lights that use a color changing LED use a parallel capacitor because the colors are changed by a tiny IC inside the LED and the IC needs its power supply to be filtered.
Look in Google Images for Solar Garden Light Circuit.

Here is your circuit but it uses discrete parts instead of the black blob: