Clothes washer only agitates on Heavy Duty. Other speeds just click.

It sounds like a bad timer, but you need to check it out with a meter. Here are some manuals: https://dl.dropboxusercontent.com/u/...c%20washer.pdf
https://dl.dropboxusercontent.com/u/...e%20Manual.pdf
https://dl.dropboxusercontent.com/u/...20Handbook.pdf
https://dl.dropboxusercontent.com/u/...ng_Machine.pdf
https://dl.dropboxusercontent.com/u/...sher_Elite.pdf
Here are some links:https://www.youtube.com/watch?v=fVE9dZODNjk
https://www.youtube.com/watch?v=oBihToN6dxs
You may also want to test the water level switch.

Upon further observation, Agitator goes in one direction only on Heavy Duty setting, back & forth on normal and delicate settings with clicking sound with each change of direction back & forth on hand wash without clicking sound (appears to operate normally) Clicking sound sounds like perhaps a solenoid making and breaking, or two different solenoids, one for each direction.Florescent over head light on same plug as washer, flickers with each click.

With those manuals and a good meter you can find out if you have bad solenoids or, as I suspect, a grounded wire or device. That's easy to find; just unplug it and with one meter lead on ground search around with the other lead until you find the point it reads closest to zero.