Glass melting furnace never stops after it's started. If it cools down it's basically destroyed so yeah, they run uninterrupted for years. Any maintenance or fixes need to account for that.
There are electrically heated glass furnaces. They work by immersing electrodes in the molten glass, which is electrically conductive, if somewhat resistive. I imagine they could use gas for startup though. The use I saw for this was in making fiberglass from recycled glass cullet.