Won't Spin 50% of the time

Washer fails to spin about half the time. Everything else works fine.

"About half the time" we find the soaking-wet clothes evenly layered on the floor of tub and much too wet to throw in the dryer.
The other half of the time, the spin leaves the damp clothes tighly pressed against the tub wall ready for the dryer.

Some observations:
1-The timer control ALWAYS appears to have competed the entire cycle.
2-During a ‘fail to spin’, the washer noise suggests that it IS spinning, However, the tub is not moving at all when viewed by carefully opening top just enough to see inside without tripping the lid switch.
3-The ‘fail to spin’ doesn’t seem to be influenced by the fast or slow spin setting; or one rince or two.
4-The ‘fail to spin’ might be influenced by load size. That is with larger loads, it ‘seems’ that the clothes are left holding more water than with smaller loads.

Inconvenient but Reliable Remedy:
Open washer and with two hands, rotate the tub clockwise until increased resistance makes rotation difficult (about 30-60 degrees of rotation). Close lid. Set the timer control to Spin and GO. It spins out just fine!
This routine works reliably!

Got any advice?

The next time the washer enters spin mode, watch it till it completes the cycle.
If it never stops running, and never spins, you have a bad timer. Timer is supposed to interrupt power briefly so the tranny neutral clutch can engage.

If I understood your suggested test, here’s what I just did…

…I set the timer near the end of 2nd rinse. When it entered the spin mode, the machine was quiet for about 5 seconds. Then a sound of water for about 5 secs followed by the sound of spin but without the sight of spin. This sound of spin then stopped afer a minute or two at end of 2nd rinse.

I repeated the above except…when spin sound began without actual spinning, I opened lid and turned the tub by hand clockwise about 45 deg and closed lid. Actual spinning began as soon as the lid closed.