A magnetic propane tank level indicator is a thermometer. It's based on the properties of a class of chemicals called liquid crystals, discovered in the late 1880s, according to educator Walter Glogowski at the Yerkes Winter Institute. By complex molecular movements, the chemical changes color at different temperatures. When propane liquid evaporates, it cools down a little bit. A small temperature difference exists between the the surface of the evaporating liquid propane and the gas. This in turn induces a small temperature difference on the outside of the tank, with a clear dividing line between the two temperatures. Placing a liquid crystal thermometer on the tank can visually indicate, by a color change, where that temperature dividing line is. The level of the liquid propane is where the temperature dividing line occurs between liquid and gas.
A piece of plastic strip is embedded with a liquid crystal chemical. You can attach the plastic strip to the tank with glue. This, however, is inefficient, because it can't be easily removed or replaced. Since all propane tanks are made of steel, a magnetic strip is glued to the back of the strip. This makes attachment and removal easy. The exertion forces needed to place and remove are about the same as a refrigerator magnet, which requires almost no force.
Since it's a thermometer, it reads temperature. Remember, a temperature difference exists only when the gas is evaporating from a liquid to a gas state. Therefore, it will display a great color change the best when the gas valve is turned on and the gas is flowing. If the gas valve is turned off, there's no flow. The temperature on the outside of the tank stabilizes and hence very little color change on the indicator strip.
Liquid crystal thermometers are widely used as forehead fever indicators and fish tank thermometers, because liquid crystal chemicals are common and inexpensive. The magnet used is also common and inexpensive. Because of these factors, liquid crystal level indicators are also inexpensive and readily available. Any home supply store or hardware store stocks them, and the cost is minimal. For example, one model, the Accu-Level Magnetic Removable Propane Tank Gauge, retails for about $5. Other models and prices exist, but the differences are minimal