In my experience you get work with tribute and function bands because you know someone, which could be a player in the band who recommends you to whoever organises the band (this quite often is another member of the band) or you know the agent for a band, but getting work as an individual (ie not a solo performer) through an agent is much less common, as, again in my experience, agents don't tend to get too involved in the day to day running of the band, they just handle bookings.
The answer, as always in music, is you have to know a guy (or girl). You could go through ads on gumtree or the like, but in my experience these tend to be amateur level bands playing a handful of gigs a year who don't know a lot of musicians. The full-time professionals I know ALWAYS hire people they've played with already or come highly recommended.
Some agencies run free showcases for prospective clients to come and see the band, some bands do them themselves, or just do a gig at a pub and invite clients.
But once you're in, you are IN. It takes a long time to get steady work but, after 7 years, I turn away about as much work as I take on.