You are correct. With a 3 terminal solenoid like the # PK5231201, the mounting hardware will serve as the ground connection. A 4 terminal solenoid like the # PK5232401 will require a dedicated ground wire from that additional terminal for this function.
When choosing between the two, I do recommend going with a 3 terminal like # PK5231201, as it simply eliminates the need for a separate ground wire, which will in turn require you to drill another hole into the trailer's frame. view full answer...