The Multi Bowl Water Feature shown here was not designed to hold any electronics. This was due to the design being primarily focused on being was waterproof as possible. To solve this problem, this base clips onto the bottom of the stem and houses a 9V battery alongside an LM2596 module for controlling the speed of the pump. There is also another connector for a solar panel connection.
The electronics for this are incredibly simple, an adjustable LM2596 Buck converter is used to control the motor speed. The switch allows the user to turn on and off the pump. The electronics are wired such that either the LM2596 or the battery is powering the device through the use of a diode. The wiring is shown in the diagram below:


The author remixed this model.
Swapped the battery to use a 9V battery instead and added a connection to use Solar Power as well.