This mobe is actually named An Inspired Spire Spirit. The 'An' does matter if your trying to use tracking. It's easier to kill than the greater spire spirits, not harder. It's on the top floor of the tower. There are eleven spire spirits up there -- 8 in the corners, two wanders, and the lord, plus a few on the staircase and a few down below. As you come through the door at the top of the stairs, the one ahead and to the right is the PH for both the inspired and steadfast ones.
Any of the greater and lesser spire spirits can sometimes spawn in a version that sees invisible. The ones that see invisible seem a little easier, as they don't cast spells as much. I always killed them first because I like to be able to cast invisibility and feel safe. The various rare named ones and the lord don't ever seem to see invisible.
When I killed the Inspired my pet had pushed it near the edge (but still a couple feet from the edge). When it died the corpse appeared down below on the ground, so I had to levitate down to loot the Book of Inspiration.