An interesting theory I read some years ago was that they were resin traders.
It fits with the overall life of Jesus - resin traders didn't enjoy much social standing in the day (think used car salesmen today) which fits with his tendency to associate with those society didn't care for. It also fits with the gifts - frankincense and myrrh being their wares and gold being the proceeds from selling their wares.
It doesn't fit with the idea that they were granted an audience with King Herod - it's not easy to see the equivalent of some dodgy used car salesman being able to land an audience with the king these days.