cave anglers

[SmokedBrisket]

To hunt them consistently are they fished up or do you just have to hope one spawns when you load the map?

[tyrtix]

hope they spawn, deep rivers and deep lakes underground...not sure if cave lamps do actively spawn them...

[flashshark]

They have specific nodes in which they spawn in underground lakes and rivers, assuming nobody loads those map tiles, I think you can check every 30 minutes or something like that. (Keep in mind that they don't spawn in all rivers/lakes.)
Cave lamps have a small chance to spawn them too when you pick them up, though I don't know how small the chance for this to happen is, probably very small.