Hello again, so far i am not trying to fix anything, disconnecting the red wire from the transformer, disables the printed circuit card, and if the fan still runs with the power off to the printed circuit card that proves 100% conclusively that the relay contacts are physically burned (welded together).
That was the reason for that test.
However, if removing the red wire from the transformer resulted (accidentally) in a 'fix', that demonstrates an *electroinics anomally in the micro processor chip on the board, those electronics are sometimes influenced at least temporarily by a removal of power.
I will comment on some of the 'why's later, and to any extent that you wish.
Now.... this above ... is my statement after a measly 51 years in the business fixing these sorts of problems in HVAC systems of all types, from home style furnaces to multi million dollar systems seen in industry and tall buildings.
It does not mean by any stretch of anyones imagination that I know what on earth has gone on inside the atomic scale micro processor chip.... those are my *presumptions after experience with these since they came out in this industry beginning in the mid 1980's.
Here are some of the 'why's however.. The integrated circuit (the 'chip') is composed of electronics sub components, so small that hundreds of them can fit in a short strand of human hair... these are primarily transistors, capacitors, and resistors... the transistors function by changing state when power is applied to its base, or not applied to its base... there can be *residual charges* that do not abate as they should at times through the resistors and capacitors within the chip, holding the transistor in a switched position that was not intended by the designer.
Where do these charges come from? Only the shadow knows for sure, they can come from static charges introduced to the circuits from outside means, such as electrical surges on the incoming power, or from even touching the printed circuit card itself (there are lengthy articles on these issues if you would like me to provide links to them, or you can search them on google).
Click here for google search results on static electric discharge effects on integrated circuits
Diagnosis of these sorts of sometimes transient conditions is not worth the time and effort in a lab and is often not more conclusive than my abbreviated note above.
However, there can also be permanent effects, some of those mentioned in this series of articles, that occurs when a high voltage static charge causes an arc between circuits that destroys one of the 'wires' (only 6 or 8 atoms wide of gold, silver or sometimes copper)
Here are a few photo's.
You can click on any of the photo's that interest you, and get to the original web site. most often university or manufacturer web sites.
Here is a good book on the very broad topic of what causes these problems in the manufacturing process, and makes chips vulnerable to later damage post manufacture, (I spent 10 years involved in chip manufacturing facilities, for intel, IBM, and Texas instruments addressing this range of topic)
Let me know if this addresses any of your questions on the topic and if not, what else you might be in question about.
We can go from there, without time limit,