A store-bought appliance timer could be adapted to suit your purpose.
To build your own long-period timing circuit there is the 4060 IC (or its cousin 4040 or 4020). It consists of a series of binary counters. Apply a clock signal from any pulse generator. Period can be once every 2.6 seconds. Outputs on the 4060 change state one at a time. You'll find that the highest (namely the most significant bit) does so about 12 hours later. Fine-tune the clock frequency as desired.
You don't need to wait 12 hours to see if the frequency is correct. Watch the lowest bit (2^4 is the lowest available pin). It should change state after 42 seconds. Then the highest bit should do so after 12 hours.
I recommendedYes, I looked at the MCU's but I think it will consume more power. For example, in the datasheet for ATmega48A/PA/88A/PA/168A/PA/328/P MCU's:
Why do you ask?The CD4060 datasheet is not clear to me. Can you please tell me if I can use 3V source voltage? I see only 5V in the datasheet...
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