Using Timer2

How do you setup (wire and program) an Arduino chip (not board) to run Timer2 in asynchronous mode from an external source so as to continue running in power-save mode?

"An Arduino chip" Which one?

Read the datasheet. It's not too hard to find that information.

My point was a chip, not a board. My source in mind is

I read the datasheet, how do you think I knew to ask the question? I didn't see any details on HOW to do it, only that it CAN be done.

Unless you have some strange datasheet it is described in the datasheet. Read carefuly the whole section about it (including register description) and it should help you.

When AS2 is written to zero, Timer/Counter2 is clocked from the I/O clock, clkI/O. When AS2 is written to one, Timer/Counter2 is clocked from a crystal Oscillator connected to the Timer Oscillator 1 (TOSC1) pin. When the value of AS2 is changed, the contents of TCNT2, OCR2A, OCR2B, TCCR2A and TCCR2B might be corrupted.

It should, but it doesn't. Can you be a little more specific? I don't see a pictorial or schematic about how to wire it. TOSC1 is the same pin as XTAL1. I'm doubting you can connect two crystals to the pin at the same time. If the OSCn pins are connected to a 32kHz crystal, how do you get the rest of the chip to run?

What happens if you connect Timer2 to a 16.0MHz, as is found on the Arduino UNO boards?

It will probably not run. If you want use clock crystal you need to run from internal oscillator.

128kHz internal oscillator? That's a far cry of 1MHz let alone the 8MHz, 16MHz, and 20Mhz that some of the ATMEga328 run at when driven external.

What happens if you connect Timer2 and the arduino to the 16.0MHz as is found on the Arduino UNO boards?

What happens if you connect Timer2 and the arduino to the 16.0MHz as is found on the Arduino UNO boards?

The external clock source needs to be 4 times slower than the system clock. See this thread

128kHz internal oscillator?

No, the internal 8MHz RC oscillator.

Looking at table 9.2. Which option does the compiler default CKSEL3...0 to?

So if I took a standard 5V 16MHz Arduino UNO, and change the crystal from 16MHz to 4Mhz (or less), then from a hardware standpoint could I use the Arduino Board as is?

Which registers would I have to reonfigure for the clock? CKSEL? How would this be done through the Arduino IDE?

You need to change fuses to change main clock source. You need external programmer for this.

The asynchronous timer's oscillator is optimized fro 32.768 kHz watch crystal. I had problems to make it run 400 kHz crystal. It will probably not start oscillating with 4MHz crystal.

Arduino UNO eats so much current (the USB to TTL chip, LEDs, power regulator) that your effort is pointless anyway.

You can run the TC2 in synchronous mode if you want clocked from main clock source. This way going to power-save only the clock source and timer will be running leading to not so much current - but far from separate clocking of asynchronous timer from watch crystal.

Adding a good external RTC results in even smaller power consumption AND more precise timing.