I think Time Mage is going to be a DPS. Of course it is just my theory, but Yoshi-P seemed to hint about the fact that Gaia hammer is important, which led some of us to think a new job will use it. The spells Gaia is using through the second part of Eden look like time magic to me. First she kills a monster with a delayed magic attack (the spell is cast, and a few seconds after the spell effect stops, it explodes out of nowhere). And then the effect of the magic she uses at the end of E8N shows a clock. + E3 had a lot of time/delayed magic attacks involved. Now my personal hope for it would be for it to be a DoT based mage, and for Summoner to be revamped to rely almost exclusively on pets.

Jester I don't know....in traditional FF job concepts, I would associate jester with gambler, which means : a lot of RNG. So I think that could become a fun limited job if anything. Throwing dices for random effects etc.

A melee healer is a popular request. I am not sure the devs would take this risk though.
They reduced the complexity of healing jobs quite a bit in 5.0 (fewer DPS spells, easier card usage etc).
Having a melee healer would make it more stressful, which doesn't seem to be something they would do.
I would like a non-caster healer though. Chemist comes to mind. Throw potions, throw bombs, throw poison bottles as a DoT. etc.