Okay, due to extreme suckitude, I believe my strategy is completely wrong. For starters, the power line that's on the serial port is 12V, not 5V. That would normally work to my advantage (wireless bridge's power supply is 12V) but unfortunately, according to this thread, this power signal goes away when the empeg is in standby. Because it goes into standby when I turn the ignition off, this means no power to the bridge. I wish I had seen that thread earlier, or I could have saved myself a lot of time thinking about this. The solutions mentioned later in that thread are way beyond my comprehension, so it looks like I'll have to use some kind of timer like the two that pim mentions.

Well, so much for that.