Restrooms appear with adequate frequency along the way. A few years ago, I drove around the whole island. While I was told the ring road was around 1400km, my car clocked in 3400km when I returned to to the rental place, since I kept taking detours and looping around to see the sights. Sometimes the sights were so beatuful that I decided not to stop the night and drove on instead to not miss anything.
The most comfortable restrooms will be in lodgings but each restaurant has one, so you have access to those facilities at each meal time. Those would be second in comfort and cleanliness.
The third type of restrooms where I stopped the most are those in areas of interest. Most waterfalls of significant interest have a parking lot and restrooms. Those are of course basic but they have paper and running water. When I was there, all of them were free to use except for one at Hraunfaussar that could be used for a small donation. It was also the only heated bathroom that I noticed, so the fee was easily justified.
Jokulsarlon is one of my favorite places but I do not remember any facilities at the time I was there. It was the middle of the night around the summer solstice but given there are boat tours provided, I think there might have been some facilities too.
Many gas stations have bathrooms but not all. In general, if you choose a station which has a small store attached, there will be facilities. Driving such distances, you would need to stop for gaz often so it would be often the case of you being a paying customer too.