Re the thermostat location, I agree - it is almost certainly in the bulge off the front off the cylinder head. Bulge clearly visible just above the water pump pulley in your lower photo.
As for how the circuit works during warmup, I continue to be puzzled. I have made a sketch of how the circuit appears to be (omitting the air bleed line which is not relevant to the cooling function).
It would seem that all flow stops when the thermostat is closed - weird! However, in practice, many thermostats have a bleed hole so that some coolant always flows.
The purpose of the "U-hose" is unclear. Is it possible that there is a flow passage internal to the header tank that directs flow from underneath the thermostat to the U-hose port? Some thermostats are actually "diverter" valves that do not simply shut off a the flow. I wonder if you have a thermostat like this.
View attachment 161640