Am wearing a French tee shirt as I write this and am therefore stylish, the "correct arm length is between a third and a half way between the shoulder and the elbow. This allows the biceps to be partially yet casually displayed.
There was a fashion for tee shirts with mini sleeves but they seem not to be around any more and were worn by bad boys.
Ebay is selling sleeveless tee shirts:
https://www.ebay.co.uk/itm/Fruit-of-...m7h1 wIGhG5ag
Not exactly a vest as a vest has a cut away shoulder, not seen anyone wearing them.