I disagree. Mearl's comments above and in a couple other places imply that it is completely impossible to "turn off" passive perception.
I see Mearls' comments as no more or less valid than any other DM which is to say that's how he rules it as his table. In this case, I don't rule it that way because it effectively kicks the meaningful decision-making back to character creation rather than keeping it during play. I want the trade-off as suggested in the Basic Rules (page 65).
Part of what it represents is your ability to hear things. If you are searching through a chest of drawers, you aren't looking behind you and you aren't watching for threats but you can still hear people sneaking up behind you and therefore still get your PP. Searching a chest of drawers doesn't leave you deafened.
Which is why the DM takes these things into consideration when deciding whether the outcome of the situation is uncertain enough to warrant a check (passive or otherwise), whether the check has advantage or disadvantage, or whether the outcome is certain i.e. the character does or doesn't notice the threat (no check).
This is backed up a couple of places in the rules. It says that a DM can rule an NPC is distracted if it is busy doing something else and therefore rule that an NPC isn't looking in a particular direction. Therefore, it allows you to make stealth checks to sneak up on the NPC even though you'd normally need cover(since the DM can rule that the NPC is looking in a different direction and therefore you have "cover"). But the rules still require you to make a stealth check vs the NPC's PP to determine if you succeed. Even if they are distracted. It is even suggested that you give a creature advantage or disadvantage on their PP if they are particularly distracted or paying attention.
The rules don't require us to do anything. The rules serve the DM, not the other way around. They come into play when the DM says so to resolve uncertainty that the DM establishes.
The only time that it is mentioned in you can "turn off" your PP is during the Exploration rules that say when you travelling long distance you can abstract the game into exploration turns that take hours to accomplish. When in this mode if you take an exploration action other than being on the look out, you don't contribute your PP to seeing ambushes.
Otherwise, you always have your PP against all traps, hidden doors, hidden creatures, or anything else as long as you are able to physically perceive it. In other words, you can't your your PP to see a hidden door if you have no line of sight to the door. You can't hear a creature sneaking up behind you if they have silence on them. But there should always be a chance to hear someone sneaking up behind you even if you are in the middle of reading a book or even sleeping.
You might get disadvantage for being distracted but it isn't going to give anyone auto success.
The rules would seem to suggest otherwise. First, and again, the DM decides whether a situation is uncertain enough to use mechanics - he or she might decide on automatic success or failure instead. As well, the section you're referencing doesn't mention "exploration turns" and earlier in that chapter it suggests that pace and travel takes place over
minutes, hours, and
days, not just hours as you say. A slow pace is 200 feet per minute. One can imagine that searching a 20 x 20 chamber for secret doors might include walking the perimeter of that room thrice (240 feet, just over a minute) while poking around. That's a task being performed repeatedly and thus may warrant a passive Perception check.
Further, it states that if a hidden threat is in rear of the party, for example, the DM may say that the front and middle ranks have no chance of contributing their passive Perception to determining if they notice it. It says if someone is foraging - which sounds not so different than "searching through a chest of drawers" - that you also don't get the benefit of your passive Perception. So while that character is tossing the room for secret doors as above, maybe he or she can't also be alert for the mimic on the wall that takes the form of a painting. I see no reason to treat these rules as some subsystem that comes into effect when the characters are walking for a minute or more. It reinforces to me that there is sometimes a cost to doing something other than keeping an eye out for hidden threats and that the fictional situation matters more than the mechanics.
In addition, it's not uncommon to see DMs struggling with characters that have a very high passive Perception - RPG forums are rife with this sort of complaint. Ruling it the way I suggest takes some of the power away from passive Perception. It means that if a player builds a character with a very high PP, they need to actually be the guy who is keeping watch, standing guard, or tapping with the 10'-pole in order to get the most benefit from their investment. They can't
also be the guy who tracks and forages and searches for secret doors (unless it's a ranger in favored terrain) while still picking up on every hidden trap or monster. This makes it a meaningful choice during play and helps with ensuring equal contribution throughout the party.
Another example: My rogue, Chuck Dagger, has a PP of 20 at 1st level. You could almost see the DM's dismay when realizing this. But as I explained to him, look, if I'm doing anything other than keeping watch for hidden threats, it simply doesn't apply. So when I'm going down the corridor looking for secret doors, I know that I could run afoul of a trap or monster. That's a meaningful choice I made, one that has potential consequences. Alternatively, I can keep an eye out for trouble and someone else with a lower PP can go look for those secret doors. This reinforces the fact that Chuck can't do it all alone and encourages teamwork. Without ruling it this way, my meaningful choice occurs only when I created the character and took Observant feat and Expertise in Perception. My way, it's both a meaningful investment during character generation and a meaningful choice during play.