The solenoid is made by GAL an Israeli company,. Motorola bought a bunch of them for their "Piccolo" irrigation controller in the late 90's (I think). I designed irrigation control equipment for about 20 years... there might very well be back emf diodes I do remember one that had them. The control circuit I designed was for 2 wire latching solenoids of the type similar to the "normal" ac solenoids however I had a circuit that "Dumped" a 4700uF cap charged to 12Vdc into the solenoid. I used a DPDT relay as a "reversing" switch and it would handle either 2 or 3 wire solenoids. I do know about polarity issues with the Gal solenoid and with the Rainbird type of 3 wire solenoids. The Rainbird solenoid fit on the valve, the GAL type was a "Pilot" valve type of valve controller. In my circuit (I made several thousand of them) the transistor switch grounded one end of the solenoid the relay decided the end that was grounded and which end was "hot". The "common" solenoid wire was connected to the capacitor (+12V end of the 4700uF capacitor) for 3 wire solenoids. My design worked with all solenoids and would drive a solenoid through a 1000' length of 16 Ga wire (from a 4700uF capacitor charged to 12V). I later used a MAX1771 to provide an 18V source that would work through about a 1/4 mile or about 1700 feet of 16 Ga wire. My pulse length was 100 mS and the cap had done its work in the first 20 or so mS the rest of the time was there for damping the solenoid (simply terminating the solenoid through a load.... the discharged capacitor).
Doc