What is the water level in the battery?
What is the battery Mfr? Model? AH rating?
Was the battery voltage at 13.2?
If the battery was fully charged.. like days on shore power, the fan should have been able to run all night and not hit 12.0VDC. Was the battery ever drained before?
The fan will draw about 1 amp maybe 1.5 amps, either way if you calculate it out over 6 hours it should only use between 6Ah's and 9Ah's. If you have (example) 85 Ah's rated, you would have only dropped to 75 or 79 Ah's, still well above the 50% rule. I would fully charge the battery at least a couple days on shore power and pull the 30 amp main fuse (isolate the battery from the TT). Take a voltage reading, should be about 13.2VDC. Let it sit for about 4 hours and take another voltage reading, the battery should be close to 13.2 or in the area of 12.9 area.
If your volt/ohm meter has an amp setting on it you can, disconnect shore-power, pull the 30 amp main fuse, set the meter to Amps (may have to move one of the leads to another hole on the meter) and put a probe into each side of the blade fuse holder. This will give you the amps being drawn by the TT. Make sure you have the fan running and disconnected from shore-power. As mentioned you will also have the other items drawing from the battery CO detector, radio ckt, fridge ckt....). If you want to know what those other things draw from the battery turn off the fan and take a reading.
You will then know how much drain you have on the battery.
Check your batteries connections to insure they are tight. Also check the negative battery cable where it connects to the frame, make sure it is clean and tight. One last thing, check the 30 amp fuse holder and see it is corroded on the inside. Pull the fuse to check that.
Let us know what you find!
Don
My Registry
RVing with SOLAR