Have I used the multimeter correct?
Readings should be obtained with the multimeter on ohms x 1 range. If using a digital meter this would normally be the 200 ohm (lowest) range
Anyhow, hold in there and we shall see.
From closer inspection of the photos you supplied, the motor is more likely to be a cap start cap run motor which is a tiny bit different from the sketch in #17 I supplied above.( missed that originally sorry)
Including the slightly different sketch below.
To complicate matters a little, again closer inspection shows some of the capacitor connections may be made half way in the motor windings which would explain your virtually open circuit readings.
What you have to appreciate is that you have the motor there with you and it is rather difficult at times for me to see what I would like to see, however we will endure.
I will see if I can track the wiring with the latest info I can see and get back to you.
In the meantime, perhaps a shot of the centriugal switch plate showing the setup ( side-on perhaps) of the switch and the link wire that goes from the back of T3 (blue I believe) to the switch support "L" bracket ( wire link looks to be about 50mm long) top photo in post #4 (btw whatever these are they magnify really well)
Can you supply the capacitor values( should be written on the body of the caps somewhere) along with their respective color cables also.