It should work, but there are a few things that must happen.
1. It must be high enough so there is enough cool water in the radiator and return line to the cylinder to outweigh the volume of hot water in the cylinder, head and uppipe to radiator. Think of it like weights on the end of a balance type scale. The weight of the cold water on the down side MUST weigh more than the weight of the warm water on the upside in order to get good flow. Making the return line as large a diameter as possible would also help here. In setting this up, I would use a bucket and compare the water volumes from base of cylinder to top of up pipe where it meets the radiator, and from top of radiator to bottom of downpipe where it meets the cylinder. You need at least an equal volume of water from the two sides. Then it is up to the radiator and airflow to maintain the weight difference that powers the flow.
2. Thermosiphon is powered by gravity and the difference in weight between a volume of warm water and a volume of cold water. The greater the difference, the greater the flow. In order to power it, you MUST cool the water. This means a good volume of airflow thru the radiator and an adequately sized radiator to remove the heat from the water.
3. To work, the rad MUST remove the ammount of heat placed into the cooling system by the engine. At full load, I would guess a 12/1 is going to need to dissipate about 36,000 BTU/HR thru the cooling system. A 1.3L suzuki Samari gets what kind of gas mileage? 30 MPG maybe on the highway? At 30MPG it would burn 2 gallons per hour at 60MPH. With gas at around 115,000 BTU/gal, that is 230KBTU/HR of heat input to the engine. Rule of thirds says that about 76,666 BTU/HR should be dissipated by the cooling system under these conditions. Better mileage would mean less BTU per hour thru the cooling system, but I don't think the Samari gets much better than that on the highway. That rad is also sized to do this job in pretty high ambient temps. At 30MPG, that demonstrated heat dissipation capacity is more than twice what you can feed it at full load from the 12/1 so the rad should work OK for you.
A larger radiator would have the advantage of larger capacity and more water weight which would enhance thermosiphon flow. It also would have the advantage of more surface area which would require less airflow to cool a given ammount of water. But a larger rad also requires a larger volume of coolant and takes up more space.
I think your suzuki radiator will work OK for thermosiphon.
Good Luck