There are all sorts of tribute bands ranging from those that are the closest you'll ever get to the "real thing" without actually going to see the "real thing", and at the other end covers bands who just play songs by a single artist.
To the OP. IMO you need to be a lot more specific about the sort of tribute band you'd like to be in and why. As others have said lots of tribute bands are formed by musicians who are massive fans of the act they are a tribute to, and someone who doesn't appear to be as enthusiastic about the music may not be the sort of musician they are looking for to complete the line-up. At the moment to being "open-minded, just nothing too heavy" tends to make you come across as being somewhat unfocused musically. With the right connections you might get a one-off dep when the band are desperate, but you'll need to be a lot more specific if you want a permanent band place. Also if you want to get into a band who are more than just covers band who only do one artist, you will probably be expected to look the part, at least as far as having the right clothes, haircut, makeup (if applicable) and instrument. Are you prepared to do that?