Question: At what distance is one able to investigate objects and/or their surroundings with the intent of identifying/finding illusions?
Context: The party is in a cliché illusion-filled dungeon. They know there could be illusions around, but aren't particularly skilled in INT or Investigation. When it's important, and they want to check before a big move, or in a pressured situation like combat, how far away can they expect to detect an illusion?
Specifics: The illusions are all being made via Major Image by a bunch of Level 13 casters with 20 INT, so the DC is (8+5+5) = 18. They are being cast at level 6 so they are "permanent." All illusions were set up before the party arrived, and all enemy casters are elsewhere, thus they have no knowledge of where illusions may or may not be. Assume the rooms/halls are all well-lit, and the party is otherwise unhindered by curses/spells/effects. The party's best Passive Investigation is too low to spot the illusions, even with advantage, thus requiring manual checks and crossed fingers.
Two cases to consider:
The party see an object/creature at XXXX feet away. They wonder if it's an illusion, so they Investigate it. At what distance is this check reasonably possible, and at what distance would the DM be fair in responding to any roll with "You don't see anything abnormal about it from here"?
The party is in an endless, straight hallway. They think the floor or walls may have a passage or pit concealed by an illusion, so they investigate. There is no object they're checking in detail; just a "search" of the surrounding area's walls and floors. If it was within 5' of them, and they rolled well, it seems unarguable they'd spot it. At what distance is this not going to benefit them?
Expectation: Looking for a RAW answer, but I'm assuming there isn't one. Therefore an educated suggestion, perhaps based on existing mechanics or similar activities, will work in the absence of RAW. Also, in addition to "how far can it work," it may also be "how far does it work without disadvantage, and then how far with disadvantage?"
Considerations: In terms of non-RAW, I had considered using a 60' limit, based on the ability of those with Darkvision to see their best within 60' of themselves. Darkness is NOT a factor for this question, but it's an example of using a sight-based precedent.
Please Avoid: This is not a question of good DM etiquette. By this I mean that, if the party were thinking the hallway had secret traps/passages, and the illusion is actually 200' away, a good DM would likely allow them to travel carefully, checking as they went, and they'd potentially spot it before they plummeted into it or passed a corridor. No "gotcha" involved. They could also do cool tricks like rolling ball bearings down the endless hallway [for some distance, not important to this question] and seeing if it fell in a hole. But this question is for technicality - suppose the wizard wants to Dimension Door down this endless, uniform hallway 500', and that just so happens to be exactly where the pit trap is. Then it matters. That's the intent behind asking the question. You may assume the players are given every opportunity to be successful without nit-picking.