A fluorescent tube will glow when there is an electric field inside the glass. Normally this occurs when a current of electricity is passed through the tube when a wall switch is turn on. The electric field causes some electrons to separate from the nuclei of the gas. When the electrons fall back into their regular places, they cause the tube to glow. This is called a "ground state."
When you rub up and down with each of the pieces or cloth, fur or plastic, you create static electricity. This static electrical field excites the electrons.
Does the tube glow brighter when a different material? Why do you think this is?
Warning: the electricity being generated is not dangerous. But be VERY careful with the fluorescent tube. If dropped, you could get cut with broken glass.
Also, fluorescent lights contain small amounts of mercury, so if it does break, put on a pair of disposable gloves, clean up the pieces with a damp paper towel, and seal everything in a plastic bag or in a container, such as an old margarine tub. The bagged pieces should be brought to a hazardous waste site or bulb collection site.