I've tried finishing this game several times during my AGS years, and I believe I have always gotten stuck at the same place. I have:
The men's room mirror, clean.
The polish.
The lens.
The key.
The water bottle, full.
The stick/pants/bird.
The mechanical eye blocks my advance. The official walkthrough says I should hit the heater button with something, but alas, have been unsuccessful thus far.
I feel much shame for never finishing this game, but have finally stiffened my upper lip as they say, and bit the bullet, and etc.
Spoiler
have you been to the cockpit yet?
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keep going down... *wink* to get to the cock...pit... *wink* get it?
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I've been to the cockpit and spoken to the floaty brain. Am I missing something in either the cockpit or the closet?
and
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I think you were referencing a rooster who must be very short.