It can take no longer than 6 seconds, since the eye rays are 1 action. Further, it doesn't matter if the DM says 1 second or 6. Once the eye ray comes out it's too late to counter it, and before that you can't see any "casting," so it's uncounterable. Counterspell requires visual confirmation of a spell being cast and Beholder eye rays have none. No verbal. No somatic. And no material.
You are conflating "what makes sense to you" with "what the rules say".
While I disagree with your conclusions, anyway, it doesn't matter because the rules do not speak on this. The idea that components are needed to see a spell being cast is introduced in Xanathar's as part of the additional optional rules for running spellcasting, they are not in the core books. Therefor, it is up to the DM, depending on if they want to use those optional supplemental rules, in whole or in part.
What the houserule in question is doing, is replacing "spell" with "spell or magical ability which replicates a spell". Since the eye rays are not spells, they never could have had components, so when introducing such a houserule, it is up to the DM to determine how the spellcasting rules apply to magical abilities which replicate spells.
It's easy to imagine that a spellcaster knows when a beholder is using an eyebeam, before the action is completed, so it isn't even a weird conclusion to say that the caster can know in time to react to it. Hell, we don't even know when the casting is done. You assume it's done as soon as any visible sign exists, but I wouldn't. If the ray fizzles due to some other ability that can stop a special ability as a reaction, my description would naturally be that the group sees the light up, the first hint of a beam like a black lense flare appears, and then fades impotently into nothing. But even if my inclination was just to describe the eye lighting up for a moment as it focuses on Bren the Artificer, that is a visible sign of the ray attack being made.
This is especially true when we consider that counterspell works regardless of what action is used to cast the spell, so the game assumes that everyone is paying close enough attention to everyone else that they see the wizard
start to cast Shield as a reaction, and have time to make the decision to cast counterspell and perform the movements to do so before the shield spell goes off.
And we know the eye ray isn't instantaneous, because reactions in general work against it. There is a hair's breadth of a moment for the rogue to uncanny dodge, or for various characters to reduce damage or give a bonus to a save or whatever.