My 21882 top load Kenmore washer will start the cycle but stops after filling up; i can restart the cycle by pushing the knob in and going a little further in the cycle then starting again. But after a while stops again. Can't get to the sping step. Is this the timer module?

Check for an obstructed washer pump or drain hose.

Bad timer. Try to find a used one if possible, this item is a little expensive.

to change water temp when a cycle has started, pull the knob and reset the water temp, then move the dial to the desired setting. push knob in. resolved by trial and error!

DOES IT DO THIS ON EVERY WASH OR SOMETIMES? IF SOMETIMES, CHECK LID SWITCH( THERE'S A LITTLE HOLE WHEN YOU OPEN THE LID, ON THE LID SHOULD HAVE A LITTLE PLASTIC PIECE THAT GOES IN THAT HOLE. THE SWITCH IS UNDER, INSIDE THAT HOLE. YOU CAN GET A PEN OR KEY TO SEE IF IT'S BROKEN.)
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you need to replace the timer

sounds like the timer to me

Sounds like the contacts in the timer has a problem. Unplug washer. Remove the back of the washer and spray WD40 in the timer. Put towels around and under to to collect excess runoff.
Rrotate washer dial 25 times and spray some more wd40. Rotate 25 times again. Do a wash load. If it works put everting back together.

sounds like motor if nothing stuck between tubs or in pump ,check these first if ok you have bad timer

if not running over ck to be sure drain is proper height and end of washer drain hose is not too tight in standpipe sound like siphoning after 1st wash and not filling to advance to rinse also be sure washer dring hose is not more than 6-8 in into standpipe

It sounds like you may have some bad contacts in the timer or you may have a bad lid switch which will not allow it to go into a spin during the rinse cycles or the final spin.