A lot of what BLU has is spells that have the same function as spells from other spellcasters (stoneskin, slow,etc)- I don't see why having a time mage which uses a lot of the same spells as other mages would be a problem - it would just be another spell list to mix and match.
I mean why is it okay for scholar to have mostly the same spells as rdm/blm/whm but not have time mage share some of them (have it's own unique list/job abilities/a couple unique spells)?
For job abilities it would be cool if they had something on a 5 minute timer that reduced the casting time/mp cost of all their spells by a quarter. And on a ten minute timer - one that made the cast times/mp half cost.
It would be cool if they had a slow spell that would gradually slow the enemy more and more over time - or a stop spell that worked the opposite - the enemy would be super slow to start with and gradually it would wear off. They could be on long timers to ensure that they weren't overpowered.
HoT would be okay to have - and maybe they could have a "random" nuke spell that varied by the game hour - and one that varied by game day.