Ok, thanks for all the details.
You answered the question on the interlink, the outback unit has its own port for the generator connection and then it is in full control at that point.
When you can perform the test, that will tell quite a bit.
The generator should run with no ill effects even at idle speed if that is all that is needed.
It sounds like there is something happening at the Outback unit that is triggering the generator and making it cycle.
This can happen if if it tries to put the generator online and then takes it back off due to some type of switching in the unit.
The hertz will also change as this is happening.
I would first, test the generator connections to see what the voltage is actually doing, monitor and record the up and down cycle as much as possible.
Then, I would disconnect the generator from the Outback unit.
Fire up the generator as a stand alone unit and try to plug as much as possible into it and monitor it that way.
Cycle the load and see how the generator acts when that happens as well.
That will be the tell tell on the situation and lead you to which is ailing, generator or Outback.
How is the generator wired? Just plug in the receptacle on the generator and 3 wires on the other end to the outback?
If the generator is being used as a permanent installation for backup power, Is the generator frame grounded outside with a grounding rod?
It should ground to the same rod as the Outback unit
Also, if you have a distribution panel for your power in the cabin, it cannot have a neutral/ground bond. The generator will have one and the Outback unit will have one, NO OTHER should be present.
This is from the manual:
If a bond is made between neutral and ground, make sure only one bond is present in the AC system at any time. The FLEXpower ONE comes with a neutral-ground bond installed. If a neutral-ground bond exists elsewhere in the system, the neutral-ground bond in the FLEXpower ONE will need to be removed. See Figure 18.