Goodman high efficiency furnace.
Furnace has been shutting off periodically, for a few hours at a time and then starting up on its own.

Sometimes when I would change the temp. it would start up again at the same time. But now...
The igniter does not glow when I restart it (after turning off the power) and it just shuts off, tries to start a second time and then shuts off again after a valiant effort.

Seems the igniter is not working. Cannot see any glow or burner flame during this process or at all. (Have pulled the back off to see better).
Is this a cleaning problem? Can anyone tell me where to start?

You will need to check a couple of things. First, look for the fuse on the control board and check it. If it is OK you will need to check for voltage at the control panel. Is the induced fan running?

Do you have a voltmeter & know how to use it?