I need help with a long pulse from a waveform

I have a circuit that I’m using which generates the following waveform for a total of 5 seconds.

I need to use this waveform (which is essentially a bumpy 5 second pulse) to turn on a 12v DC power supply (from a car battery) for 12 hours. Yes, hours. I thought of using a 555 timer as a monostable multivibrator, but they are only good for up to 10 minutes. I need the 12 hour “on” state to be accurate down to +/- 1 second. Oh, and I need this to be as efficient as possible since it’s a battery powered application.

Any suggestions?

Yes use Arduino to detect pulse on one pin and then use another pin to control FET that switches the 12v

Use millis to detect when 12 hours (43,200,000 miliseconds) have elapsed. Then turn off FET

I had thought about that, but without a real-time clock connected, how reliable is millis over a 12 hour period?

And can you give me an example of an FET to purchase? I haven't used any before, so I'm not sure if there is a typical FET used.

For 12-hour delay, a digital scheme like millis() should be about 100,000X times more accurate [rough guess!] than using any kind of analog device like 555, which uses RC-charging.

Look for a "logi-level" MOSFET, meaning the gate can be driven with 5V; non logic-level MOSFETs require 10V drive. Something like IRL540, the "L" indicates logic-level.