Although continuously waking the Arduino and blinking an led every few seconds is a possibility, I fear that method in the end will use more power than just connecting a very small, led directly to the battery and just let it run.
How do you work that out? - having the LED
ON all the time drawing 1mA (for example) takes 1mA on average. Using the processor to flash the LED with 1mA for a second every ten seconds only averages 100uA, a 90% saving - so the battery will last ten times as long. The power the processor uses is far too small to bother about, as it's in sleep almost all the time, and only wakes for very brief periods.
You also don't need to flash it for as long as 1 second, much shorter is perfectly acceptable, and easily noticeable.
You've got an Arduino?, it has an LED on the board - try flashing that from sleep (consult the link I gave above) and measure the current taken. Experiment with ON/OFF times to see what you consider a good indicator, and then try an external LED, and alter it's series resistor upwards, until you get minimum current with acceptable brightness.
I usually use PIC's, and for longest battery life I use an external 32KHz crystal on TMR1, which wakes the PIC every second - I usually then update the 'real time clock', and check for whatever the device is supposed to be doing, then go back to sleep. This only takes microseconds - and battery life is likely to exceed the shelf life of most batteries - so we use special long shelf life Lithium batteries. Five+ years should be easily doable.
For less critical uses I just use the internal clock, modern PIC's have
LOAD'S of clock options, and usually wake the device every millisecond, and keep a millisecond count running, as well as an RTC. Although power consumption is higher than the external 32KHz option, it's still stupidly small