Ok, here is my thoughts (disclaimer, I have a 64 so there may be some differences):
For the horn, was there a custom steering wheel/horn for 63 and do you have one. If so it may be the hardware holding the horn in place. On these there is a plastic ring that contacts the concave metal flex plate. Without that it will never work (been there done that). If it is not a custom steering wheel/horn I would still start at the concave metal flex plate. If this thing is not shaped properly it will impact how the horn grounds when you press the horn button. Make sure that when you install the three screws/plastic spacer the concave metal flex plate is still free to move. Also, it should be installed with the dome up.
For your dash lights and gauges, get your schematic out and a probe with a light in it to verify voltage. Activate each switch and confirm you have voltage (the light goes on) both going into the connector and at the back of the dash. You may have to pull the dash out a bit to get some clearance.
One thing you can try for the dash lights is to replace the light switch. I know this doesn't seem to fit but I had a situation once where the high beams worked but no low beams, turned out the internals of the light switch were worn out. And check because you may be able to get one from O'Reilly's or similar without spending a lot or waiting for shipping.
