Dangerous liasons

I recently bought some facial cleanser, actually cleansing milk, if you want the precise term. On the bottle was written

Visage et Yeux (Face and Eyes)

in case I had any doubts as to which body parts I was supposed to use it on.

Eye is a funny word in French. The singular is oeil and I can't even describe how to pronounce it and I don't want to bore anyone with phonetic symbols. Anyway, it's a funky word. Un oeil, l'oeil, le troisième oeil...

The plural is yeux. I know. Ridiculous. Completely illogical. That one is pronounced with an initial y as in yeah sound followed by a vowel we don't have in English. The x, like many final consonants in French, is silent. Because y is a y, if it is preceded by a consonant, that consonant is pronounced, even if it's usually silent. Bear with me.

For example, les yeux. The s in les is only pronounced if the following word begins with a vowel or a y or an unaspirated h. Don't ask. Anyway, yeux is nearly always used with an article in front of it. Des yeux or les yeux, or deux yeux bleus. Which means that it is always preceded by a [z] sound, because final s and x are both pronounced as [z] in cases like this. This process is called liason.

So, when I read the bottle, over and over, I couldn't imagine how in the heck to say it correctly. You can't put the [z] in just gratuitously, there's no article in sight. But you can't leave it out because it just sounds so strange. And you certainly can't liase the [t] because that sounds even stranger.

I asked a few native French speakers. Without leading them. I wrote down the phrase and asked how they would pronounce it. No one could give me a straight answer. None of them wanted to add the [z] because there was no article and no one wanted to pronounce without because it 'hurt their ears'. (Seriously, two people said that.)

Which made me wonder if the [z] hasn't become a part of the word yeux now. A silent partner, if you will. It's always there, even when there is no evidence of it's being there, other than the feeling of offness.

Who's your silent partner?