What has me interested in pet battles again is that I've been doing daily world quests and emissaries on 5 or 6 different toons, and there are always a few pet battle world quests out there that are relatively fast way to knock out a world quest for that zone.
When pet battles first came out in Pandaria, I originally didn't do anything with it, but then during the year-long bore-fest of Siege of Orgrimmar, I decided to dive in and get as many achievements as possible. So I gathered all the wild pets, beat all the trainers, defeated all the Beasts of Fable and got through the Celestial Tournament.
Then when Draenor came out, I sort of forgot about it again and haven't done much with it since. I didn't even get far enough along to unlock the level 3 pet menagerie in my garrison.
So I'm thinking about going back and trying to get caught up on Draenor, Legion and Battle for Azeroth pet battle achievements. I've collected almost nothing in terms of wild pets from any of those expansions, so getting that alone may take a fair amount of time. In any case, it's a way for me to stay engaged in that content lull between expansions. Particularly if I'm just not in the mood to level a 43rd toon to 120.
The other thing that I've done periodically when these lulls occur is PvP. I'm less likely to go that route this time because I did a ton of old school AV during the anniversary event and really got my fill during that process.
I am almost done with the mage - he's just started on the Battle for Azeroth zones, venturing in Drustvar at level 111.