"Well there's your problem!"
The white wire has a slice in it that seems to have corroded over time. I ended up cutting out a section and soldering in some new wire. I now have working hazards and power antenna.
I also found a larger gauge blue/yellow wire that was also damaged. Per the wiring diagrams, it goes to the ignition switch. I repaired that wire as well, and noticed a significantly stronger/faster starter. I'm guessing there was a voltage drop across the damaged/corroded section of that wire. Glad I caught that one before it completely corroded through.
Thanks for your help everybody! 