To test the starter solenoid.... when it clicks in, check the voltage that exists at the large battery terminal of the solenoid. That same identical voltage should exist at the other large solenoid terminal that leads to the starter. If so, regardless of what that voltage may be, the starter solenoid is okay.
Dual Engines...... If you're using the same battery to start both engines, and one starts normally... then obviously the battery is okay. In either case (single or separate batteries), running good known jumper cables from a good known battery directly to the starter will tell you if the starter is at fault or not.
If you're sure that the battery and starter are okay, the cause of the problem is usually a loose cable/wire or a tight but dirty cable/wire end terminal. Remove and clean the terminal ends of all cables/wires associated with the starter system including the actual battery terminals. Also clean the components that the cables/wires attach to.
Let us know what you find