To be certain of your description…. when you say you replaced the “master switch” ….I understand you replaced the switch in the panel that provides a “ground” to your battery master contactor/solenoid. And that had no effect.
You also are saying that energizing your pull-starter seems to remove power from all items… but that “recycling” your cockpit switch sometimes seems to “cure” the problem and the starter will rotate the engine….(which then presumeably starts to run, the battery is re-charged, and everything works properly.)
You are asking if there is a simple method to determine what is causing this problem…and your hypothesis is that the battery master contactor/solenoid is not passing sufficient electricity to the starter unless you re-cycle the cockpit master switch…… the question being “is there a simple test to see if your hypothesis is correct?”
Am I correctly understanding your question?
If I am…. then there is a simple method to by-pass your battery master contactor/solenoid…. and that is (staying CLEAR OF THE PROP….. use ordinary automobile jumper-cables and connect the large terminal on one side of your battery contactor/solenoid to its opposite large terminal. You have now completely by-passed that battery contactor/solenoid …. the main electrical “buss” is active….and pulling your starter should activate the starter.
Replacing that battery master contactor/solenoid is not expensive. Depending upon your comfort-zone…at Spruce you can source the part for as little as $32 for an automotive equivalent …
https://www.aircraftspruce.com/catalog/ ... kkey=10293
. or as much as $80 for one that claims to be better:
https://www.aircraftspruce.com/catalog/ ... kkey=10293
So, for $32 you can simply and temporarily replace your present contactor/solenoid with one that will prove or disprove your theory (instead of using automotive jumper cables)….and if that works for your test…. you can “forget” to remove the $32 unit and probably never have to deal with it again.
OR…you can buy the $80 unit, install it and achieve the identical happy results.
Why puzzle any further about your questionable contactor/solenoid when a solution is so inexpensive and be done with it?
PS: if you do this yourself…. please DISCONNECT your battery ground-strap while working on the solenoid. Recoonect your battery ground strap after the new solenoid is installed.