Since the Rav has shown that the prohibition of lighting a fire on Yom Tov is NOT Nolad (as usually is heard), but rather the prohibition of doing anything on Yom Tov that could have been done before, how about lighting a match (to light a stove or barbecue), if one did prepare an existing fire, but it became extinguished. (This actually happened to me on the last day of Pesach). Similarly, could one turn on an electric light, if a child turned off the existing one?
The logic that he should have done it before Yom Tov is the reason behind the Issur of Molid Aish.
You are correct. If the fire goes out or the light is turned off, one may relight / turn back on.
See Ohr Yitzchak Vol. 2 #217