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“why the fluctuations up and down?”
The wire capacitance is being varied by inductive reaction to the surrounding environment. This could be nearby signals, close proximity objects, the orientation of the wire to ground.
Usually if your cap meter is set too high (sensitive), it will indicate these variables to the extreme. It is like turning up the gain of an amplifier, which a cap meter basically is an amplifier calibrated to indicate a reading corresponding to capacitance. Same is true with a meter measuring resistance or voltage. There are basic designs with less sensitivity and others that have a wide sensitivity. This is why some measurements call for a good DVM, those have an increased sensitivity compared to the basic types such as simple analog meters.
If your conducting measurements of this kind within the same room as the “window” antenna and its emitting RF energy, along with any other signals being generated, nearby lights and ballasts, that measurement will be influenced by these external sources acting upon that wire.
The effect can be observed when tuning a 3 meter antenna setup. As you move closer to the antenna, it is affected by inductive capacitance from your body, and the resonance will change a bit, and change again as you move away. That is why some of those all in one box transmitter units recommend a non-conductive, non-inductive tuning tool. Same is with aligning a sensitive receiver front end or transmitter intermediate stages with a non-conductive and non-inductive tuning tool.
Any wire, be it in a coil form or straight line, is subject to external influences and thus will react and measure accordingly.
Take a regular capacitor and connect it to your meter. Set to measure. Then take your fingers and “pinch”, or grab the capacitor with two fingers and note how the meter changes its reading, perhaps even change as you get closer to the capacitor. The more sensitive the meter is, the greater the influence rage will be and in turn would be affected at a greater distance from an external influence.