I am not one of those audio gurus,,,but don't they use a capacitor to prevent parasitic draw.
You have the classic 'lights dim when sub hits'. the ballasts need a constant even flow of juice. they probably both went into protect mode.
I heard that is the horn and whatever. You would probably have to track down a harness diagram,,,,I have seen it but can't remember where.
Either way your SUB is more than likely breaking the weak links. Nothing takes more juice(sound wise) than anything say below the honk of a 250hz note,,,let alone 80hz and down
If you have an EQ, roll off some of the lows......get rid of most of the 50 and down,,,,maybe you can get by with a more tuned low end end.
Most people crank the 100 and down, just because. you really can't hear it as much as feel it(and piss off the neighbors).