Could be. But I thought a microprocessor, with its support components, would be overkill, too costly, for a cheap consumer item. Especially with such simple function.
there's plenty of microcontrollers that'll run on anything between 1.8 and 3.3V and need no external parts, eg: ATTINY4-TSHR or PIC10LF320-I/OT under a buck in small quantities, much cheaper in lots of 100000 as bare dice for chip-on-board construction.
"what's the timing circuit"
It's a microcontroller, the clock is probably the on-chip RC clock, it's slower to turn off possibly because the designer intends that behaviour as a warning that the batteries are low. it's better (and easier) to warn of low batteries at turn-off
Chances are good that it may be some dedicated IC in there. If someone an cook up enough demand, it's simpler for a dedicated IC than everyone working on their own.
I have some single LED "bicycle lights" that are smaller than a 9v battery and you attach to the handlebars with the included elastic. They cost $3.75 Canadian. The first one I bought, it had slow flash, fast flash and steady on, you'd press the button and advance the mode, then another press ona off. The mroe recent ones do away with one of the flash modes, so it's only continuously on or flashing. At that price, you can't spend much time adding parts to a circuit board, so chances are good it's dedicated to it. For all I know, it may be what's used in the bigger LED bike lights, which of course have a similar ability to flash and stay on, and use the on/off button for the same function.
So if it's a dedicated IC, chances are good as much as possible goes in the actual IC (which would just be an expoxy blob).
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