The only "houserule" they will need on the spot is if you stop attempting to hide, or have nothing to hide behind, and enemy can find you.
That's it. And as has been pointed out in this thread REPEATEDLY, nothing actually states that the only possible way to find someone is to take the search action. In fact, we KNOW it cannot be the only way because we know of other conditions or situations which would break the stealth without the enemy needing to take the search action.
Even though I know this will only be used as a "see, this is totally broken" let me show you what I mean.
View attachment 375145
A is a Wizard
C is a bat that is the Wizard's familiar.
B attempts to hide from the Wizard. Per the rules they can, because they are not in line of sight of the wizard and they roll a 17. The wizard, getting a sense of danger from their familiar who sees a knife being drawn, uses their bonus action to use their familiar's senses.
B cannot hide from C. They don't have cover, so they cannot hide from them and C absolutely sees them.
By the current interpretation that you absolutely need to take the search action to find a creature that hid from you, and the fact that the wizard only used their bonus action... suddenly C stops being able to see the creature that hid, who is now completely invisible to them. Which is nonsense, because the wizard can now "somehow see" them and has found the intruder. And even if you want to argue that because it is the invisible condition and B miraculously became transparent from their hide action.... Bats have blindsight and can see them anyways.
And no one who is approaching gameplay in good faith would ever state that using their familiar doesn't let A see B.