According to IMDb, Connery tried to incorporate a ponytail into his hairpiece and arrived on set with it. In an alleged interview with Sight and Sound Magazine (we can't find the actual article), director John McTiernan was enraged that the actor would try to strong-arm his idea for the character by going over his head.
Connery's Marko Ramius would have sported the cool new look throughout the film, but the director of photography laughed and said it looked like a "limp, swinging d---," which became a joke among the crew.
This upset Connery enough that he removed the ponytail after the second day of shooting and had to reshoot a scene.
Even weirder, he would go on to sport a ponytail in "Medicine Man," also directed by McTiernan.
We have no idea if this one is true, but it's funny.