"The rest of the time he mostly slept."
Translation:La ceteran tempon li plejparte dormis.
hiding right before our very eyes. Now I can guess that it translates to "and continuing..."
I don't understand your question. To what extent is your question not answered by the original sentence and by my discussion with RandomCanadian?
The definition in PIV is Restanta, ankoraŭ ne menciita. It's what's left over or which hasn't been brought up.