Light is actually well-suited for a Burst build since it has access to Affliction resistance down, which is built into Tsukuyomi's Elemental resistance down ability. With Shingen+ Sniper Shot, Sol, Light Tsukuyomi, Diana/SSR Artemis, and Michael, you can reach -40% ATK (-50% with eidolon) and -50% DEF. If you wait for Sphinx to be ready before Burst and debuff reapplication, debuffs missing shouldn't be a problem in most encounters.
The main problem Light has is that it needs to run Sniper Shot or sacrifice -ATK or -DEF, and therefore won't usually have access to Black Propaganda. Raphael (subbed for Diana/SSR Artemis and used with Vine) can mitigate this issue somewhat by making a Rage Overdrive less likely before the Burst. Light can also run Amaterasu instead of Diana/SSR Artemis to free up the EX slot for Black Propaganda. This will reduce damage, but once Shingen gets her Relic weapon that doubles Burst damage, the loss won't matter as much. Giving up on the class B debuff entirely and running with low -ATK like a Fire team, once SSR Artemis is available, is also an option due to Light Tsukuyomi's excellent Blind.