Maytag top load washer intermittently won't stop agitating

Hello, We have Maytag top-loading 2 speed washer, model number is LAT8340AAW, Serial #A4103334, that has been acting up lately. At first it would occasionally miss the spin cycle and fail to turn off at the end of a Normal Fabrics washload and continue for a full revolution of the dial (i.e., when the timer-dial reaches Spin, the machine doesn't spin and empty, but continues to agitate. When the knob is pointed toward top of the circle (OFF) the machine doesn't always shut itself off, but the knob will continue turning over to the Permanent Press side while the machine agitates -- full of water). If we stop the machine and turn the dial around to rinse or spin , it _usually_ finishes the process correctly, spinning, emptying and stopping. This doesn't always work, though. Occasionally it won't spin on the second try. When it has failed to spin, manually opening and closing the lid has twice twice allowed it to go from agitation to spin. Tonight that did not work, but giving it a 15 minute rest (turned off), was followed by a successful spin, drain and shutoff.
This started as an occasional problem but has become more frequent. We try to always wash on the slow speed. Advice would be much appreciated (in as much detail as you care to go into).

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