Figured it out - it's because I haven't done the MSQ "Far Edge of Fate" yet. So I'm about 10 MSQs away from hitting that, and only then will the next Summoner Job quest pop up - a level 60 quest that will probably be 11 or 12 levels below my current level by that time.

Seems like the issue is - because I'm doing the patches and expansions after the fact, I'm WAY outleveling the gatekeeping. I ran into this on my Dancer as well - I hit a wall in my job progression that couldn't be resolved until probably weeks or months of MSQ progress. So I mothballed her and switched to other classes.

I guess you really do have to focus on the MSQ above all else, and then circle back to do other things...