If your battery is reasonably charged and the alternator/regulator stops putting out, the voltage should not go down to 9 volts even with the load of the lights, fan etc. The battery should keep the voltage up at least for a time.
Where are you measuring the 9 volts or are you looking at the dash guage? Does the battery go dead?
You may have a bad alternator/regulator but you also must have a bad connection somewhere probably close to the battery or.... everything is fine and the guage is acting up. Check voltage with a real meter. If intermiittent you could hook it up in the cockpit to some point that carries 12V, perhaps the lighter and observe while driving.