I had this problem in my car too after installing megasquirt (but not before megasquirt, even with the 80-amp alternator) and I have a slightly different theory on why this happens.
When we install megasquirt, we are all usually wise and use a relay to power MS and the ignition circuit (EDIS/etc). However in the original 2002 electrical system, the ignition coil was powered DIRECTLY via the ignition switch (key), and NOT via a relay! The coil is a big load, and in the factory setup when you cut out the battery by turning off the key, the little bit of juice from the alternator at idle isn't enough to power the coil.
There is enough juice at idle though (especially with the bigger alternator), to keep the RELAY energized! So while the relay stays energized from the little trickle from the alternator, your ignition circuit is still being fully fed from the battery.
My solution was to use a 15W light bulb as a load in series with the relay so that there is enough voltage drop that the relay will switch off when you turn the key off. You could also use a power resistor, but I like the added light in my engine bay from the light bulb! (Remember though, you need a load to dissipate the extra power from the alternator, so a regular low wattage resistor won't cut it. Load is the key here, not resistance.) All that being said, I'm sure a diode would work fine as well if it's in the right spot and doesn't get burned up. I didn't use a diode because I never figured out through what path the relay was staying supplied, but that dash light does sound the likely culprit. Hope this helps some people!
-Carl