My relay is not on during starting (although obviously the ignition is). 
It also isn't on with the ignition on but the engine not running, or
running at low RPM.  

It seems the supply voltage must be up to a certain
point, and there may be a slight delay factor, too. It appears to me that
the relay is there to make sure that the considerable load of the 12v
fridge is not applied during starting or if there is not enough alternator
output to carry it. 

Dave Garth