I keep all my tungsten in a little hand made holder with a bunch of holes drilled in it. This holds them pointy side up so they don’t get dulled before I use them. I also don’t have to keep getting up to sharpen each time a point gets dirty.
To sharpen them, I use an old variable speed drill, chuck one up, then spin it slowly as I gently hold it against the grinding wheel. I always sharpen with the tungsten pointed up so there’s no burr on the end.