Fill shower trap when it gets empty with water pressure
Here is a possibility but I'm not sure it would work in practice.

You'd need a container which could be sealed so that water will flow out the bottom when the end of the hose is uncovered, but when the cap on the container is secured a low pressure will develop on top of the water in the container. This is the principle used for animal water bowls which replenish a tray from an inverted container.

I can imagine a plastic jerrican with a hose coming from the bottom. Fill it and the water would fill the tube and start flowing. Then screw on the sealing cap and a 'partial vacuum' will develop above the water. When the pressure goes down to a certain level the water flow will stop.

When the trap is drained and the end of the hose exposed, bubbles of air may move up in the tube and increase the pressure above the water in the sealed container. The diameter of the hose is critical--it must be large enough for bubbles of air to move upward through the water in the tube all the way to the container.

You may  find that adding detergent to the water in the reservoir would enable bubbles to form and move up the tube when the end is uncovered. The detergent lowers the surface tension of the water and allows bubbles to move up the tube.