Dexterity in playing a musical instrument is all about muscle memory, not looking at the fingerboard. After all, you’re meant to play the violin while reading a score. And the fingerboard is in a rather awkward position to be staring at all the time anyway.
So, if there is no score around to be read, having your eyes open or closed doesn’t make any difference to how you play; and having your eyes closed helps with concentration, and figuring out what you’ll do next.