The diagram on Page 19 of
this manual indicates Dometic used a two-way capacitor. One side for Compressor (may be marked "HERM" for Hermetically Sealed part of the A/C, compressor, coils, etc.) and the other side for the Fan. Coleman tends to use use two separate capacitors with their common terminals wired together. Same thing. If you find one side of a two-way capacitor is bad, you can get a single of the correct value and wire the Fan or Compressor to that side alone. From the diagram, it seems the Brown and White wires from the Fan Motor lead to the Fan Run Capacitor or part of the two-way capacitor.
Please understand, it's not the Capacitor(s) every time one of these things won't run. But it Often is. If an RV A/C has a leak, a damaged coil (condenser or evaporator), a clogged expansion device, or a bad compressor, it's junk. What's left, where repair could be economical, is Fan Motor, Fan Blade/Blower Wheel, Capacitors, Switches/Thermostats etc. Anything that's not HERM.
If God's Your Co-Pilot Move Over, jd
2003 Jayco Escapade 31A on 2002 Ford E450 V10 4R100 218" WB