Washer drains as it fills

I can not find your model number that you posted.
I can tell you that all whirpool thin twins up to last year were direct drive with no belt except for the dryer section. Whirlpool stackers from the early eighties did have a washer belt if yours is this old replace the entire machine.

try to keep the drain hose above the height of the washer, as it may be siphoning out

Based on your discription you do need a new timer.

the timmer is bad, replace the washer due to the cost of the parts.

make sure drain line is vented.

Is your drain at the proper height? I will attach a photo showing the minimum drain height requirements. Have you moved or changed the location of the washer lately? If not let me know so that I may consider another cause. Thanks and I hope this helps. Best wishes.

If the cycle does not stop draining that is usually because of a faulty membrane switch that controls the water level in your appliance.
The faulty sensor cause the machine to think that there is still water inside, even when water has drained completely.

check lid switch

Make sure the tub us actually moving. Sounds like the belt may have come off. That is what has happened to me.

yes you do have to remove the top off the washer and the washer should come with a mounting kit that must be used when stacking this unit. as far as your filling and draining problem i have had this problem several times before you have to replace your speed control board or sometimes called the speed control unit in the lower right hand corner of your washer