In an old thread I did a pretty massive breakdown of Intellego sense spells and how they interact with MR. It boils down to 'sense' vs 'magic sense'. The first is just a spell that moves/manipulates your senses around while the second is a spell that creates a non-natural sense. The second is always affected by MR while the first often is not [once species leave the Parma, they have no MR]. The ability of 'sense' magic to often ignore MR does not exist for non-sense Intellego spells.
TDE is a 'magic sense' that is not dependent on species from the target. It does not matter if the species from the target are altered or destroyed, it is the magical ones being projected by the caster that do the work. For an invisible target you would see both their original and invisible images, meaning just their original, if you penetrate. If you don't penetrate, then you will see a "dark spot" in the magical aspect of vision.
Invisibility spells normally use the PeIm Base 4, which only destroys their Sight Species. InIm Base 3 "Enhance" to Sight would not help you since it works by manipulating species and there are none to manipulate. However any spell that can detect the other Species at a distance can overcome Invisibility (baring a higher PeIm Base). You could use InIm spells which use a sense at distance with a Range of Voice or Sight.
Touch is the one that normally make most sense for this type of spell. Hearing can be defeated by the target staying still and Smell will not always differentiate enough. While you run up against the targets Parma for Taste and Touch, Touch will give you a blank Magus shaped spot if it fails to penetrate while Taste might not be able to distinguish no taste from the taste of the air.
InVi Base 3 "Detect regio" is not detecting species being destroyed and is worthless for detecting an invisible target. However any of the InVi Bases which detect active Magic would detect the invisibility spell if they penetrate MR (and the invisibility is high enough Magnitude for the Base used). Spells that detect Vis could also indicate something is off if the target is carrying any, though it would have to penetrate MR. Spells that detect the Gift would also work if they penetrate MR.
Not just Eyes of the Bat but most Intellego Form Target: Sense spells that do not depend on the Species of the invisible thing could work. As above, some would have to penetrate Parma and some would not so choosing ones that do not is best. You also want to choose ones that give you the finest grained sense.
EotB does not have to penetrate Parma and is a very fine grained sense. Even in Sagas where Parma could effect it, all that would happen is that you detect a Magus shaped blank spot rather than a Magus.
Sight of the Molting Magus (the spell right above The Discerning Eye) would have to penetrate to make the target glow, but any leavings from the target are outside of their Parma and so readily apparent to the caster. How useful it would be on failed penetration depends on how much activity has happened in the area recently since the spell gives an estimate time of separation.