Single pilot reported a NMAC with a flight school aircraft while at cruise altitude. The pilot stated the other aircraft was traveling the opposite direction and not communicating. The reporter took evasive action.

Narrative

I was cruising on autopilot @ ~3500 direct from ZZZ1 to ZZZ2. Although slightly below 3000ft AGL; had targeted 3500 ft for cruise altitude because of SSE direction of flight.Approaching ZZZ3; re-set altimeter per automated weather and was @ ~3450.Saw on Foreflight another aircraft at same altitude approx 8-10 mi to the ESE; seemingly heading almost due westerly and pointing directly toward my aircraft.I changed radio to the ZZZ CTAF; which appeared to be the airport the other aircraft had left and that we would next be passing by. I announced my altitude and location and direction of flight. I also checked to see that I had all my lights on incl. strobes.I thought that possibly I would pass in front of the other aircraft but then it veered slightly more southbound; almost as if tracking me. My Foreflight continued to show it at same altitude. It appeared from its speed that we would at minimum near collide. I could not see it visually despite frequent to constant scanning.As it closed to 3 miles I began to take evasive action; turned off altitude hold; and climbed approx. 400 ft.During the climb I finally spotted the plane and it passed directly under my plane at an estimated vertical distance of 200 ft - 400 ft below.Later study of tracking on two sites showed that at approximately that point in the flight the other aircraft had a very brief climb and then drop of approx. 400 ft.At no point did I see a landing light or strobes wile the plane was approaching.A day or two later I looked up the owner -- my iPad Foreflight had shown the tail number -- which was a well-respected local flight school operating out of ZZZ; and advised them of the incident.Technically the other plane was at a legal cruise altitude; but I expressed my opinion that it is not optimal in the busy airspace to be cruising west at 3500ft which is likely to be an altitude Eastbound traffic will be at. Also; I wondered if they had seen me; at least on the traffic-ADSB-in device I could see their plane had. Finally; I suggested that lights on in this airspace was a good idea even tho not required; just to aid visibility. I never received a call back from the owner or instructor.I assume the other aircraft did not see me visually or electronically until late if at all. The sun would have been to its left and ahead. However the blip in altitude change at the spot where we nearly intersected makes me think that; belatedly; I appeared on a device or was spotted. However; since altitude change was my only option; the other plane's similar climb was ineffective. I had radio'd my position; had lights on; and had filed a flight plan before leaving ZZZ1. Not sure what more I could have done. I did not have flight following on because in that airspace it is very distracting; but possibly; if the other plane was also on; a controller could have coordinated our movements.The improvement that occurs to me is that; while there are protocols for head-on approaches; there is no default evasive maneuver for converging aircraft. The other plane here was supposed to give way; but what should the pilot in my position do if the other plane does not turn away? Climb or descend? It would be helpful if there a default protocol.Also; in areas that are above 500 ft MSL but not much above that; much activity in the busy airspace occurs at altitudes of 2500 ft-3500 ft MSL. No one at those altitudes is required to fly at VFR cruise; but I think it is best practices to assume eastbound may be at 3500 ft. So when I am flying west at 3500 ft or below; I try to stay at 2500 ft-3000 ft to give a minimum 500 ft from anyone at that height. Similarly; when eastbound I try to avoid 2500 ft if 2500 ft is not possible due to cloud cover. I don't think a rule addition is necessary but it could be advised as a precautionary measure.Finally; my first flight school had a policy of maximum lights on when a student was at the controls; until off runways. While taking care not to blind other pilots; using lights even in day can only help; esp. with the often hazy air around busy urban airspace or popular training schools.