Almost certainly this is because a bad wire. Specifically, take a look at the wires coming out the back of the alternator. If one of these wires isn't connected (I can't remember which one), most of the dash lights come on. In your case probably all the insulation has crumbled off the offending wire and it is shorting out.

It really has nothing to do with mashing on the gas, other than the engine twists on the mounts a little bit when you do this. This is probably enough to short out this wire.

So look for crumbling insulation on the wires coming out of the back of the alternator. Good luck!