It sounds like you have two separate gremlins here to me.

Are you are describing the three red warning lights faintly glowing on the instrument panel?

That is most likely that famous 86 crap wire insulation on the little red wire on the alternator or a worn set of brushes in the alternator.

Check the condition of the red wire on the back of the alternator and then on the big connector in the center of the firewall. There four wires from the connecter that go through Intake Manifold 3 & 4 and separate. The red and black run under the engine, the red to the alternator, and the black to the oil pressure sending unit. The other two wires break out right under the manifold, the yellow black goes over to the temperature sensor on the block, and the blue/yellow to the starter solenoid. I battled the connector and it's wiring for years and kept having issues. Ended up going down and buying a male and female trailer hitch wiring set for less than $6. There are only four wires in the center connector and any other connector I looked at cost over $20. The wires were long enough to reach everything and you just have to splice the four wires on the drivers side. A good shrink tubing and tape job on the splices should put that problem to rest once and for all. You will need to reuse the oil pressure sending unit connector, the other three wires just need a blue spade connector.

The other cause would be a set of alternator brushers going out, you can quickly take off the negative battery post and with a phillips screwdriver replace the assembly in just a few minutes. Onkel is right about checking or just out right replacing that ground wire from the Alternator housing to the engine block. Might as well pull out the proton pack and blast as many ghosts as possible while you are in the area.

The only way I can think of for hitting the brakes and getting the dash lights to come on is for it to be a ground issue also like Onkel.

Those are not even on the same circuit is the reason for thinking it must be a ground. The Brake lights are on an unswitched circuit (fuse 7) and the dash lights come off fuse 1 to the rheostat. Are there any other lights out on the dash besides the instrument panel ones? For instance is the light in the gear shift on when the are out? They do have their own ground separate from the other dash lights is the reason I ask. The ground for those lights comes out on the half moon connector the back side of the instrument panel and it's the black wire. That would be what to follow to check the ground and most likely those goes to the dash ground in the center dash.

It never hurts to shine up all the fuse holders and make sure the contact on the fuses are nice and bright. Have read about several strange issues that seem to originate over there.

Good Luck with the Volvocism,

Paul