The external fan is controlled by a simple snap disc thermostat affixed to an outboard cooling fin on the upper condenser. It might be bad and it's easy to replace and replacements can be had on Amazon, Dell Electronics or DigiKey.
You do need to determine what it's rated for temp wise however and that will rake a look see to determine.
The external fan could run constantly, depending on the ambient outside temperature in the outside fridge cavity and of course how hot it is where you camp. Lots of factors impact the fan on and off sequence.
On mine, the fans tend to run all day and shut off at night when it's cooler. I say fans because I added one, 2 or 3 is better than one in this case...and yours.