You are having starting issues with your jet ski and have checked the battery and it’s connections and have tested the starter solenoid/relay. What next? It is time to look at the start/stop switch.
First, check the wires for any that are loose, disconnected or damaged.
To test the start/stop switch on a jet ski you will need a multimeter. These are fairly inexpensive at places like Harbor Freight.
Set the multimeter on Ohms and put one lead on one each side of the switch.
It should read open when the switch is not pressed. When the switch is pressed it should read closed and no resistance. As the switch starts to wear, it can read minimal resistance, usually less than 20 ohms. If it is reading 20 ohms you have a bad switch.
If your battery, starter solenoid/relay, and start/stop switch all test good ….. it is time to replace your starter.