The bar will keep fix as the bracket is tight. Tape is only for protect the curtain from stuck in the while opening. Even though it never slide and stuck.
Does this curtain rod makes light come through the sides as I have my bed in the same set up as you and the light is getting in my nerves at the moment.
In my arrangement like this, the light is still there just a little, still okay, even though I'm using the blacked-out curtain. This window is sunrise side. there are many spaces between the edge of the curtain (up, down, left right) that make the light still minimum.
