There need not be any rule that specifically says you have disadvantage.
By RAW, circumstances can impose disadvantage on any check.
You usually gain advantage or disadvantage through the use of special abilities, actions, or spells. Inspiration can also give a character advantage. The DM can also decide that circumstances influence a roll in one direction or the other and grant advantage or impose disadvantage as a result.
I mention this because I'm going to argue that the rules justify applying disadvantage here, even if they don't overtly require it.
Heavy obscurement is strictly more obscuring than light obscurement.
This is the part you're not going to like, so let's get to it.
Both kinds of obscurement are defined largely by example, and the sets of examples are parallel: Dim light, patchy fog, and moderate foliage are lightly obscuring; darkness, opaque fog, and dense foliage are heavily obscuring. The examples clearly show that heavy obscurement is like light obscurement, only more so.
Therefore there should be no case where anything is more visible under heavy obscurement than it would be under light obscurement. Anything that you can't see in dim light, you also can't see in total darkness.
The Hiding rules say that being heavily obscured has an effect.
One of the main factors in determining whether you can find a hidden creature or object is how well you can see in an area, which might be lightly or heavily obscured, as explained in chapter 8.
Finding a hidden creature involves a Perception check, so there must be some impact on the Perception check (or the Stealth check, but note this also applies to a hidden object, which likely wouldn't get a Stealth check).
The check doesn't automatically fail.
This point was made in Xirema's answer, but to restate it: detecting a creature's presence doesn't require sight and therefore doesn't always fail under blindness or heavy obscurement.
(Except when it does. A creature like a dormant gargoyle might give no signs of its presence except that you can see it, and if heavily obscured, would be truly undetectable.)
Light obscurement imposes disadvantage on detecting a creature's presence.
Perception checks that "rely on sight" have disadvantage in a lightly obscured area. (Note that the rule isn't "require sight".) Most of us could locate another person in a dark room by sound, but as a practical matter we rely on sight to do this.
Conclusion: the Perception check to locate a heavily obscured creature must be at least as hard as rolling with disadvantage, but there's no rule that it's any more difficult than that. The game mechanic that best fits in that space is to roll with disadvantage.
Finally, I think this needs to be said:
The text is not written to be used this way.
You say that you aren't interested in what the rules are intended to do, but that's essential context for reading them at all. The Player's Handbook is a handbook. It explains how to do a thing, namely, how to play the game. It is not a legal code or a set of tournament rules.
None of the rules mentioned here rigorously define their terms. In particular, the obscurement categories are specified mostly by a handful of examples. We had another question going recently about whether partial fog and dim light combined count as heavy obscurement, and the rules give us no way to answer that.
Similarly, if you're blind, you automatically fail "any ability check that requires sight", but ability checks don't say when they require sight. You have to figure that out case by case.
There are also some consequences of this situation that are far more obvious than "disadvantage on Perception checks" but aren't spelled out in the rules. For example, the Blinded condition says you can't see. This causes you to automatically fail at checks that require sight, but what about, say, reading a newspaper? There isn't a check for you to automatically fail, but still, you can't see. To grasp the implications of the rule, you have to apply logic and experience.