That's exactly what I did in both cases. Gave the customer the choice of paying for a new timer (more money, delayed repair) or do a field repair at less than half the price and done right then.  

Yes! You have snatched the pebble— that’s exactly what I’m showing. These are real-world skills with real-world results. No more of that awful sinking feeling, muttering to yourself, “what the heck is going on with this circuit.” No more schematics looking like spaghetti but instead seeing them as the indispensable troubleshooting tool that they are. 

Ahh, Grasshoppah, you have indeed snatched the pebble from my hand! This is a great question because it gets into basic electricity and circuits— exactly what I was trying to show in the video (though not that particular question). But to answer it, we need both the schematic and timer chart.

In the video, I was working with the paper tech sheet in the control console (which I replaced when finished) that had both the schematic and timer chart.  Both are needed because they work together to tell you which timer contacts are closed when. I have not been able to find a good quality PDF of both the schematic and timer chart. If you have one, please post it so we can look at your question. 

Found a schematic and timer chart for another Maytag Neptune dryer model number that is very close to the one in the video and exactly the same as far as the motor start and run circuits. I've included two schematic markups: one showing the drive motor circuit ready to start and the other shows the drive motor circuit while running. 

The drive motor Line path remains the same between ready to start and running. But the Neutral path changes. The keys to understanding the Neutral path changes are:

1. Seeing how the drive motor centrifugal switch changes the circuit
2. The timer chart for timer contact 3, the pull to start switch. In particular, notice that contact 3 is only a momentary contact as shown on the timer chart (no blackened squares for contact 3). 

3 minutes ago, Craig Knight said:

Would it be appropriate to indicate a note inside the dryer for the next technician that the line to the motor is “Hot at all times”?

The next technician better be YOU!

But seriously, what technician will disassemble without first unplugging? 

Jumper wire on the timer is self explanatory and would not require a label, IMHO. A tech seeing that should know to consult the schematic to see the function of the jumper in the circuit.  

Writing a note on the tech sheet or drawing in the field jumper on the schematic may be worth doing so you could remember what you did when you go back for a different repair on that dryer. 
 

These types of field repairs are always done after advising the customer and getting their consent. In this case, customer didn't even know what the wrinkle guard was or that this even existed! (Probably most techs don't either).