I have repaired/rebuilt many, many 261Cs, and a number of 362Cs. I work on them more than any other saws. Mtronic and Autotune saws are good saws, you just have to trouble shoot them differently.
First off, if the saw has a black solenoid on the carb, throw it away and replace it with a white or green one and also buy a spare. Also be sure to put the orange fuel filter on the saw. Nine times out of ten that fixes a starting problem on Mtronic.
I have never seen that little solenoid “kill the spark”, but I’m not saying it couldn’t happen. I have never seen the ignition coil just quit on a 261C, but again, it could happen.
Look at the bottom of the ignition coil where the two wires from the coil to the carb attach. There is a small screw that holds it tight. I have seen that be loose and give you the symptom you are having.
It sounds like you know how to ring out the wire harness with an ohmmeter. Just remember, if you have an intermittent connection in the harness, you may make the connection “good” when you take a connector loose to check it.
Also, are you real sure it isn’t a carb or gas problem? My experience with 261Cs is that the spark is almost impossible to see unless you are in a dark room.
Every time I fixed a “weird” starting problem on those saws it ended up being something simple.