Blower on my G20Q3/4e-100-5 won't shut down. Runs constantly. Heat comes on and off as planned but blower stays on, except when thermostat is turned to auto, that seems to be the off switch.

I assume your saying the blower or heat will not work when the fan switch is in the auto position? I would start with the blower control. If the burners come on but the blower doesn't. I would say you have a control problem. A bad board. Its just a guess not knowing how your blower is set up.

Maybe I`m reading your post different than T Top. I`m reading that your tstat is set at on or fan on setting
And that your furnace comes on and off as it should but the blower runs all the time.
Well as long as the tstat is set on the fan on or on setting this is what's going to happen. It is supposed to run all the time when set this way.If you want it to run only when heat is needed ,you will need to put tstat setting on the AUTO mode. This is where most everyone likes it

Yes. The blower runs in the tstat setting "on" and while blowing heat I switched to "auto" the blower quit and would not restart for some time. (I waited two hours before I tried again and was successful in turning the blower back on) I switched out the tstat (to a honeywell) some time ago and that did not help.