A question about disembodied monsters and blinding spells on them

Question

I am running a campaign with clerics, wizards and shadowcasters.

One of the characters, a cleric, wants to choose an invisibility spell. This is not the problem.

The problem is how this spell works when there is a Shadow monster next to him.

Do incorporeal creatures like Shadows, Wraiths sense living beings and how does that affect the person who is under the influence of the invisibility spell? Do they sense that person or not?

Invisibility

Illusion (Glamer)
Level: Brd 2, Sor/Wiz 2, Trickery 2
Components: V, S, M/DF
Casting Time: 1 standard action
Range: Personal or touch
Target: You or a creature or object weighing no more than 100 lb./level
Duration: 1 min./level (D)
Saving Throw: Will negates (harmless) or Will negates (harmless, object)
Spell Resistance: Yes (harmless) or Yes (harmless, object)

(Player's Handbook p 245)

Answer 1

Incorporeal creatures can sense adjacent foes, but have no special ability to see them.

The incorporeal subtype provides creatures with the ability to sense foes in adjacent spaces (h/t Peregrin Took):

It can sense the presence of creatures or objects within a square adjacent to its current location, but enemies have total concealment (50% miss chance) from an incorporeal creature that is inside an object.

Neither the undead type, the incorporeal subtype, nor the creature descriptions for Wraith or Shadow, provide any additional special senses beyond this except for Darkvision. Some monsters do have such abilities - for instance, Glabrezu and Balors are continuously under the effect of True seeing, as the spell. So this is where it would be noted if these creatures had such an ability.

With no mention of additional special senses, we have to assume that Invisibility works as normal - it prevents the Wraith or Shadow from seeing the invisible character, even though it can sense their presence.

Fortunately, we have precedents in the rules for what happens when a creature can sense the presence of something but not see it; this is the difference between blindsight and blindsense.

So the Shadow or Wraith should know that the adjacent character is there, but be unable to see them, forcing it to attack with the 50% penalty for total concealment.