Cessna 177 pilot reported an NMAC event in the traffic pattern with a non-reporting intruder landing on a conflicting runway. After landing the reporter contacted the other pilot who seemed confused and uninterested about the event.

Narrative

My aircraft had not been flown in over a week and I planned to stay in the pattern at ZZZ for a few touch and goes. Skies were clear; winds were light; and traffic in the pattern was light. There were a couple of other aircraft in the pattern utilizing Runway X. During the pre-flight; I set the altimeter to that announced on ASOS and completed my radio check successfully. Other aircraft were announcing their intentions and positions in the pattern for Runway X. I taxied and took off from Runway X and landed to a full stop. I taxied back to Runway X and departed for my second lap in the pattern. I climbed to 700 ft. AGL before turning left crosswind for Runway X. I do recall the setting sun in the west as I climbed to pattern altitude of 1666 ft. MSL. I established and announced my left downwind Runway X on CTAF. At mid downwind I ran my pre-landing procedures. All position reports were made on CTAF. As I approached the point where I am parallel to the Runway X numbers; I glanced out toward the runway and at that point saw the other aircraft had passed under and behind me. Vertical separation was less than 200 ft. and given the plane had just passed under me I would estimate horizontal separation was less than 300 ft. At that point I continued on the downwind which I extended and turned left base for Runway X. I kept an eye on the aircraft which landed on Runway XX. Knowing the other aircraft was on the ground; I continued east of the airport at pattern altitude and rejoined the pattern for Runway X at the mid downwind point and landed on Runway X. After landing and securing my aircraft; I tracked down the other pilot that passed under me in the pattern. I asked him if he didn't hear the other aircraft in the pattern announcing they were using Runway X. He seemed unaware of other traffic. I asked if he even saw my plane in front of him which indicated; 'no' at which point I expressed my concern. The pilot did not have English as his first language based on his accent. He seemed a bit confused. I asked the fellow at the ramp who shuttled him from his plane to the FBO if he noticed anything peculiar about the fellow. He indicated; 'he is not all together there.' How the problem arose: 1) Pilot of second aircraft not have a situational awareness of traffic at the airport before landing. 2) Pilot of second aircraft crossing mid field at pattern altitude despite aircraft on Runway 2 while he was landing Runway 20. 3) As pilot landing near sunset visually looking west into the sun prevented clearly seeing aircraft. 4) Other pilot did not give way to my aircraft which would have been approaching.