The Comic Strip has more footage of his early work there that they haven't put up yet - https://www.youtube.com/watch?v=snV_tfey4vE

In that clip you see images of several sets of Eddies there.

Talking about recording his first album at the Strip - https://www.youtube.com/watch?v=m9OuqmGdX5Q

From their website - http://www.comicstriplive.com/index.php/about-us/

"Originally the Comic Strip featured comics, singers, magicians and novelty acts. Soon they realized that stand up comedy was the only way to go and the Comic Strip has been a showcase club ever since. The first big star was box office legend Eddie Murphy. The first time Eddie came into the club, he was only 18 and had a lot of swagger...almost too much! Saturday Night Live soon followed and the rest is show biz history. Eddie in turn discovered Chris Rock at The Comic Strip."

The Carson set - https://www.youtube.com/watch?v=w1TKGtai7og

Kinda obvious from the vids, what Eddie has said about his start in stand up and what other comics say, that dude put in work.