The number of tags you can input in the tags section for your youtube video is the wrong question because youtube does not care how MANY tags you have but, rather, how many characters you can have in the tags section. The answer to that is 500 characters.

The next natural question is should I use a lot of short tail keywords/tags or fewer long tail keywords/tags for my youtube video. Which is better for seo? The answer is always long tail tags/keywords. In fact, nowadays, with so much competition online, all your tags/keyword phrases you are targeting for your youtube videos or any piece of content you are creating should be AT LEAST 5 words long or more. You can find keywords like this with Infinity Google Keywords.