There are several possible causes.. That pattern however sounds strange.
Atwood says to disconnect a RED WIRE from the ECO when winterizing
That would set the fault light but the cicks would not happen
Sounds to me like the fault light is programmed different from my Atwood (It only came on after the control board was assured it was not lit)
It usually tires three times than faults.. But each control board model is differnt,.
Things to check
The gas valve.. is it getting voltage and drawing current?
is the valve clicking
The Spark gap, Do you hear the sparks?
IS gas flowing (Oriface can get clogged. a spider loves the smell of gas)
Spark gap
Then it gets expensive
I had to replace control board.
Home was where I park it. but alas the.
2005 Damon Intruder 377 Alas declared a total loss
after a semi "nicked" it. Still have the radios
Kenwood TS-2000, ICOM ID-5100, ID-51A+2, ID-880 REF030C most times