Jeff,

As you figured out, the black is momentary ground from the horn ring. Brown should be 12V full-time, even with the ignition off.

I would disconnect the brown from both horns and check for 12V from the loose end of both brown wires to ground -- the chassis of the car, not the black wires. If that's not there, you've found the problem.

If you do have 12V there, check for ohms from the black wires to chassis ground -- it should be an open circuit (infinite ohms) until your assistant presses the horn ring. Then it should read close to 0 ohms. If that's not there, your horn ring is not making contact.

I'm not sure if it matters which terminal gets the black and which the brown, but you won't blow anything up experimenting. Do the left horn first with the right disconnected and try it both ways if both of the tests described above check good.

All the foam spacers do is keep the horns from shorting to ground.