You mentioned the device that automatically "Switches" from 12 volt to 120 volt.
No such device exists.
There are two different types of converters (These devices CONVERT 120vac to 12VDC and a couple different types of INVERTERS, which convert in the INVERSE diirectin.. I'm thinking you have an inverter.. Something like my Prosine 2.0 more on that in a mintue.
In the converter department. The old Magnetek 6300 line did, in fact switch over selected loads (light bulbs for example) from battery power to converter power. However if you have one of these.. Get a better converter, Modern converters do not switch from 120 to 12v. They operate in parallel just like the Lights on your car, (towed) when the engine is off, they run off the battery, when the engine is running , off the alternator, but the systems are in parallel, there is no "Switching" at all.
However in some modern INVERTERS, such as the Prosine 2.0 They monitor line voltage (120vac shore or generator) and if it is present and WITHIN SPEC they pass power on to the down-line 120 volt things
if the shore or generator power is either 1: NOT present or 2: Out of spc, they will switch over to battery power and invert it to 120vac.
Now,,, Generators come in assorted flavors.
The popular Honda or Yahaha, Kipor, Champion and ____ Fill in other makes____ Inverter generatrs generally put out good, clean 120vac well within specs, It is s true sine wave, nice and sharp on a scope, looks good and sweet and the inverter senses "Good power" and passes it.
Shore power. likewise is usually within spec (not always as it turns out) usually not as clean as an inverter generator either.
A good fairly large generator,, The exmple I'm going to use is the ONAN 5500 (Though here to the _____ applies, it's a long list) tend to be nice, clean and well regulated as well. The prosine should pass them no sweat.
However many of the portable "Contractor" type generators, these open frame, 3600 RPM shaft speed, portable ear buster generators are even noiser on the power line than to the ear drum.. The waveform is nothing at all loke a nice sharp sine wave, more like a wolly catapiller is crawling on the scope, the harmonics are way beyond 120 HZ and voltage may be spiking over 1,000 volts peak to peak (instead of 120 * 1.414)
The inverter senses "Dirty power, bad power, STAY IN INVERTER MODE" and does just that.
That may be your problem, Are you using a contractor's type generator, or a quality low speed or inverter type?
Home is where I park it!