Wait, careful about making an assumption as to the "because", until you've tested and traced a couple more more items. You may be right, but the process of thinking through the diagnosis can easily be tainted if you already think you know what the problem is.
A voltmeter will tell you mountains. Attach to cigarette lighter, or any fusebox terminal-- the basic system voltage should be the same no matter where you test. 12.6V indicates a fully charged battery, engine off. With engine running, a functioning alternator should provide at least 13.5, probably 13.8, maybe even low 14s. If the battery has been really run down recently such that the alternator is doing a great job of bringing it back up in a hurry, mid 14s isn't unreasonable.
It's a little hard to imagine that the voltage drop caused by a dome light energizing is enough to trigger audio shut-off circuitry, unless you've been running the battery down below 11V or so... and if so, I suspect you'll find out pretty darn soon when there's not enough juice left to start the car.
- Erik
64 Valiant, 170 3-spd
82 Volvo wagon, 5.0 5-spd :)
