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If the convection element has continuity then the element itself is definitely good, which means that the element is not getting the needed 220volts or else the oven would be heating. That being said there is absolutely no way to test the convection fan motor without uninstalling the entire double oven. As to one of your other questions, no the convection element does not need to heat for the fan to function properly. At this point you know you need a new relay control board because the convection element tests good. Hopefully this will also solve your convection fan issue as well. But again there's no way to know 100% for sure without pulling the oven and testing power to the convection fan motor.
I do also want to say that if your light switch isn't working and the light doesn't turn on and off when you open the door (which you never mentioned) a bad door switch could cause this problem as well because the fane and element will not turn on if the oven doesn't think the door is shut.