Time Mage should be caster dps. Rememeber in past FF games Time Mage had spells like Demi/Quake/Meteor/Gravity/Stop/Banish/X-Zone/Slip/Comet. they had some support spells too like Regen/Refresh/Haste/Slow, but those could be retooled to recover MP, and boost spellspeed or slow/gravity targets. Even Old, which could be like SMN's Virus. LB3 could be Time Compression (since BLM's have Meteor).
Just not sure what kind of weapon they'd use. I want to say maces/clubs but since mages don't melee in this game really, it wouldn't make a lot of sense. They would have to make a new type of Sundial/Hourglass/Chronometer something. They could use Astrolabes which are bit different than Starglobes.