Andy Watson:
I checked and pretty much convinced that the flicker is done right at the LED (right on the internal die, itself).
Too difficult to check for printed part numbers; my age advancing so fast, even a big magnifying glass, out in the sun, cannot read any printing, on the low profile black plastic 4-pin. So I assume thats the commonly seen charge control and boost circuit, taking the 1.2 V nimh battery voltage up to about 2.4 V.
That flicker is ultimately done right at the LED.
The in-line package has to be more than just a transistor, as it does the oscillation, and the comparator that enables running the voltage boost oscillator (plus a low to mid pwr output transistor).
So, that little 4-pin SIP is what I've seen virtually everywhere, in small Solar Lights.
By the way: The oscillator mentioned runs at some hundreds of Khz and maybe a good candidate for operating a string of counter / click dividers. Eight stages of binary counter gets that higher frequency down.... to some 509 hz to 2,000 hz (depends on original osc speed).