Although there is no Accepted Answer (probably because the person that made the question forgot or didn't know how to do it), this one is accurate, mainly the head line:
Perception is for observation, Investigation is for deduction.
From PHB 178:
Perception. Your Wisdom (Perception) check lets
you spot, hear, or otherwise detect the presence of
something. It measures your general awareness of
your surroundings and the keenness of your senses.
Investigation. When you look around for clues and
make deductions based on those clues, you make an
Intelligence (Investigation) check. You might deduce the
location of a hidden object, discern from the appearance
of a wound what kind of weapon dealt it, or determine
the weakest point in a tunnel that could cause it to
collapse. Poring through ancient scrolls in search of
a hidden fragment of knowledge might also call for an
Intelligence (Investigation) check.
On the same page, we have a Finding a Hidden Object box that states
When your character searches for a hidden object such as
a secret door or a trap, the DM typically asks you to make a
Wisdom (Perception) check. Such a check can be used to find
hidden details or other information and clues that you might
In most cases, you need to describe where you are looking
in order for the DM to determine your chance of success. For
example, a key is hidden beneath a set of folded clothes in
the top drawer of a bureau. If you tell the DM that you pace
around the room, looking at the walls and furniture for clues,
you have no chance of finding the key, regardless of your
Wisdom (Perception) check result. You would have to specify
that you were opening the drawers or searching the bureau in
order to have any chance of success.
Generally, Wisdom checks depend on your senses and instinct, while Int checks are about your thinking and mind, as Page 6 from PHB:
Measures: Mental acuity, information recall, analytical skill
And from the same page
Measures: Awareness, intuition, insight
Looking for something is a perception check. Trying to deduce where something is is an Investigation check.
Now, what you've asked in a comment was
"How does one adjudicate the potential to use two skills to accomplish the same task?" - I will first define (in my way) two different things:
- Finding an object is a goal.
- The combination of finding an object and how you are going to find it is a task.
By my definition
Skills don't dictate your ability to accomplish a goal. They dictate your ability to accomplish a task.
For the sake of an example, you could be an awful climber and still get to the top of the mountain - if you fly, teleport or just take the least inclinated path.
In the finding an object situation, you could even find it without using any of these two skills - you could intimidate the BBGE after punching his face to near-death and make him tell where his hidden treasure is, or you could find a map that includes the hidden rooms and traps, anyway, you can accomplish any task with an incredible amount of ways.
If you want to find an object by looking around, you are calling for a Perception check. If you want to find an object by trying to deduce where the BBGE would have hidden that powerful magical item, you are calling for a Investigation.
So, the skill being used depends on how the player words their action, not what they are trying to accomplish with that action.
I'll try to exemplify with the following scenario:
Player: I search for any hidden door in this room*.
DM: Roll perception.
Now, for investigation:
DM: You notice there are scratches in the floor near to a wall.
Player: I try to deduce if these scratches are made by the opening and closing of a hidden door.
DM: Roll investigation.
Note that, usually, investigation rolls should rely on some kind of evidence (since you are trying to deduce something from evidence), and this evidence is found by observation. This might seem like Investigation is useless, but that will depend on the DC you are putting on each roll. The evidence to something might need a (considerably) lower roll to find than finding the thing itself, and then the investigation roll could be slightly lower DC as well.
Another example for combining these two skills are: you might use perception to find holes in a wall and investigation to deduce these are from a Dart Trap.
In the edit, you want situations where the investigation can be used without a previous perception. Well, first you can give away the evidence as my example states, without actually needing a roll. Other than that, it is actually hard to make a deduction without evidence, but
Player: I want to deduce if any of these lockets is a good place for hiding a magical item.
Player: I want to deduce, by the layout of this building, if there is a hidden room.
DM: Investigation roll.
I should note, however, that Investigation is a less usefull skill than perception by default. Actually, perception is arguably the most important skill in the game.
If your players use the words look, search, spot, or anything that is relying on their senses, it is a Perception roll, and, by default, that is what they are going to use in most situations. Investigation will only be used in specific scenarios with specific wording from your players' action. If you are in doubt, probably go for Perception.
As you noted in a comment, finding hidden objects is not the main purpose of Investigation, nor Investigation is the usual roll for finding hidden objects. It would only be used in particular situations.