My story really quick, I live in a loft in a pretty good condition, but it does have some leaks around windows every now and then. I have used some special cock to fill the cracks - but you know water it always finds it's way somehow. I want to put some really heavy duty duck tape (Black or dark brown, as the color of the windows around it) on the top of the cock to minimize the possibilities for water drips. Again I am not talking about any crazy water leaks just minor. Also I know you'll say this is just a bandage and not a permanent solution, but i am renting and unless the landlord decides to fix the outside of the building, anything will be temporary. Any ideas what would be a really good tape that can last several years more or less.
To answer your question. Tape will not help. a good sylicone Chaulk will be the only thing that could stop the water. You may have to remove your old chaulk first .
Keep in mind that the only thing you are doing is traping the water inside the walls which will rot the walls and or become moldy which can be harmful to you. You need to make sure the landlord knows of this problem and what you are doing. The landlord can sue you for damages if you can't prove that you told him about it. if you did tell the landlord and he will not fix it. NY has a 411 service that you can call to get information on how to make him.
A temporary fix of a couple years ...I gotta write that down...I feel like Auntie Bea...chaulk and cock are things which will not help...one will wake you up at sunrise, the other is good for murals on the driveway.
A good silicone caulk will help temporarily. The good stuff is good for 50 years according to the manufacturer, but you need something to attach it to...the rotting building like guyod said will not do.
My opinion is to contact the owner, then the 411, then move if nothing is done.
Sorry for being nit picky, I'm home with the flu and needed some off humor. Nothing personal, just tryin to have some fun.