The diver basically demonstrates the relative compressibility of gas over liquid, and increasing pressure with depth. Unfortunately, over time, the simple version will also demonstrate expansion and contraction of gasses with changes in temperature (sinking to the bottom if the water, and air in the diver, cools). Eventually most divers will also demonstrate increased dissolving of gasses under increased pressure. (Greater pressure inside the diver than outside, because the gasses are supporting the weight of the diver, causes gasses to dissolve and leave the diver, and the diver to sink.) The simplest diver can be made with a jug full of water, an eye dropper or test tube partly filled and a thumb sealing the top of the bottle. More elaborate systems involve a large sealed container with pressure signals sent through a rubber diaphragm and a thermostatic heater to maintain constant temperature. The diver can include a rubber diaphragm to prevent dissolving of gasses.
My diver also demonstrates an analog to varying DC voltage, voltage pulses and AC of varying frequencies, combined into one signal. Besides the usual lever to send quick pressure signals, there could be a screw adjustment to change the bias pressure.
The diver I made started with a rectangular clear plastic bottle commonly sold in variety stores. It included lead in the bottom for ballast so that a larger air bubble would mean more movement of the rubber diaphragm. The container was a one gallon mayonnaise jar frequently found in restaurants. The middle of the metal screw-on cover was cut away. A rubber diaphragm was glued to the glass rim and what was left of the cover screwed on to keep the diaphragm in place. The temperature was controlled by a button-type thermostatic switch and resistor for a heater, covered with styrofoam and glued to the side of the jar.
The claw worked fine. The object it picked up was a plastic "marble", not very heavy under water. Unfortunately, I found that the jar was too small for easy maneuvering, and that fins on the side of a basically vertical diver aren't very effective. I went on to other things before finding a good way to build a horizontal version, or maybe a horizontal "keel" around the sides. I leave further construction details up to the next would-be oceanographer.