It appears the tank vent may be reacting to the fuel and hardening. I had some issues with my saw running and did a diagnostic teardown. Luckily I found an air leak under the cylinder before I did any damage. So I while I had the cylinder off I ported it, and did a vacuum/pressure test on the assembled motor. I found that a piece of bike inner tube sandwiched between the heatshield and exhaust port works great. I just shoved a grease syringe into the intake boot. Ran the saw and it flamed out. I did a vacuum check on the tank and it showed it was sealed and not venting. I poked a small drill bit thru the tank vent and it starting sucking in air. I tried to clean it up but it seems a bit too tight, so a Stihl one will go on order. With the twist part of the drill in the vent it can suck air thru the drill flutes and runs great.
Another 361 tip, don't lose the washer/gasket between the carb and the rear housing. It has been on backorder for months . Not sure it really a necessary part but I made a new one out of cardstock. Hutzl does have them for 59 cents.