Hello Arcai,
This boss "Imperor" Summon 0-2 Diabolic Imps,
If someone Lures out to the entrace this summons you probably can know if this boss its respawned or not,
but this is something "forced".
I feel like Naturaly Imperors will spawns in the east of the seal and you have go there to check if is there or not.
The only boss that you can check without "risk" is Handmaiden, you can walk in the top of the roof and count how many hands you have there.
Normal respawn: 6 hands Boss: 7 hands (remember they can be invisible)
I hope i helped you,
Gleemody