To answer your question as when to perform an engine fire test , have a look at General part before SOPs . It states that : "items marked by asterisks are the only steps to be completed after a transit stop without flight crew change. Otherwise the new flight crew perform all the items".
ENG FIRE test does not have an asterisk so it needs to be done on every flight crew change , that might be the N th time of the day during the last 24 hours , it does not matter.
obviously , MEL takes precedance . If for instance you had " ENG FIRE DETECTION LOOP A on ENG 1 " , item 26-12-01 A , it states to perform the engine fire test before each flight . That means even during a transit stop without flight crew change , you are stil required to perform an engine fire test