I discovered this strategy a few days ago. The fastest way to cap exp and lights in abyssea is through the use an entire pup alliance.
9 automatons set to DD, 4 set on cure, 4 set on black magic and 1 set on ranged for pulling.
Automations landing the killing blow are awarded and "enhanced" light, it increases the acquiring of lights significantly. The pups should not engage at all only letting their automatons fight, if any non automaton lands a killing blow, the entire chain is reset and so are all the lights. Also, the ranged automaton has to pull or it will break chain as well. Using this strategy the group was able to cap exp in 1 hr.