Illusion spells are typically cast on either a single living subject (T or LOS) or a physical location (LOS(A))
Illusion spells are typically opposed by potential observers (in some cases the only observer is the subject itself).
Silence is cast on a
location. If you cast it on a
location close to a wall then any observers get to oppose the spell and if they fail they will not hear hear stuff that happens close to the wall. This spell can not be cast on a
subject.
Invisibility is cast on a
subject (a person with a living aura). If you cast it on a subject then potential observers of the subject get to oppose the spell and if they fail they will not see the subject. This spell can not be cast on a
location.
This spell makes the subject more difficult to detect by normal visual senses (...). Her aura is still visible to astral perception... An invisible character may still be detected by non-visual means...
Non living observers are unaffected by mental illusion spells (such as hush or invisibility). Potential non living observers of a physical illusion spell (such as an ultrasound sensor in the case of a silence spell or a recording surveillance camera in case of an improved invisibility spell) use their object resistance while opposing the spell.
Supplements add a few illusion spells that specifically target a specific type of non-living objects rather than a location or a living subject, but they explicitly mention this (for example decoy which is the regular chaos spell but this spell only work on a non-living sensor objects - that will oppose the spell with its own object resistance rating).
Object gets to resist with Object Resistance, then what happens.
The subject does not resist invisibility or improved invisibility at all.
Any potential observers, such as a surveillance camera in case of the improved version of the spell, get to oppose the spell if the subject get into its line of sight.
Can you suddenly see through a wall in front of you?
You don't target the wall. You target a living subject.
If an observer fail to oppose the test then the observer will not see the subject (and will still see the wall behind the subject).
Can you see a target that has full cover because the cover is now invisible?
You don't target the cover. You target a living subject.
If an observer fail to oppose the test then the observer can't see the subject no matter if the subject has full cover or not.
I'm the GM, always the problem......trying to find all the crazy stuff so when it pops up I know how to handle it.
The reason we have a GM is for the GM to step in and make rulings to prevent shenanigans that the rules might not fully cover in the first place.
Having said that;
IF you rule that you can also target non-living objects without an aura with the invisibility spell
THEN you resolve it with a spell casting test and any potential observers get to oppose the test (but not the wall itself).
IF a potential observer fail to oppose the spell
THEN he would see what is behind the wall (but the wall will still prevent astral perception and targeting spells on the other side of the wall and barrier rules apply to indirect combat spells and firearms) and he would also see a target hiding behind cover (there will be no cover to obstruct sight if you attack but again, barrier rules still apply).
For the mental variant of the spell you would perhaps only see what you 'think' is behind the wall.
But for the physical variant of the spell light would bend and you would actually see through the wall.
https://www.tfltruck.com/wp-content/uploads/2019/01/valeo-invisible-trailer-camera-2019-ces.jpgBut note, this is not RAI (and I would argue nor RAW) and would probably be considered a house rule. You also need to be prepared for that this line of ruling potentially also opens up several other strange situations that you would have to deal with as well...
The
supported method of looking behind a wall is the clairvoyance spell.