Glass fuses have a low thermal stability and shatter in high-heat conditions. Ceramic fuses, on the other hand, can withstand high temperatures and are more thermally stable. Ceramic fuses, unlike glass fuses, are also often filled with a filler like sand to prevent the formation of a conductive film. When there is a short circuit, the fuse element melts and vaporizes. It deposits on the inside of the barrel or body as a film. In a glass fuse, the body continues to get heated and the film begins to conduct electricity, thus rendering the fuse inefficient. The sand in a ceramic fuse, however, absorbs the heat energy and prevents the fuse from heating and therefore conducting.
You are correct, T is for time delay and TT marking indicates even a longer time delay. I am not sure what they are using that fuse for but since it's only rated at .5 amps of current, its not related to any of the electric motors. It's more common for a glass fuse to fail vs. a ceramic fuse. I am sure they chose a ceramic fuse because a ceramic fuse can handle vibration much better than a glass fuse.
That is a fairly small fuse so it will not take much to cause it to open. Since your fuse is a slow blow rated fuse, it will take more than a half amp of current for a longer period of time to open so it is quit possible it happens again. However you will never know if the fuse was simply faulty unless it opens again. With a glass fuse you can tell a lot by looking at the filament and the glass. You will never know without waiting it out with a ceramic fuse.