Red Mage could have multiple job prerequisites. You might need to level GLD, THM, and CNJ, to unlock the RDM. Make the weapon of choice a Rapier, and you got yourself a RDM.

I was thinking what a Time Mage would need to equip in order to be a TIM/TEM, and thought a pocket watch or an hourglass would be cool. A pocket watch being much cooler.