Probably best way to attack sponsorship is to start out as a privateer by forming a team name, paint up in team colours. Get out there and race, get a few wins under the belt if you can and start to get noticed. Get talking with others in the industry. Push to get some media coverage and get some public facing pics/articles written about the race/your team. Start asking around to companies that might like to been seen in the sport and take whatever they are prepared to give you. Give them heaps of big coverage for it and go from there.
For a new series you will have to start off small and work up. Remember, a scooter series budget should not be big initally and because you are doing it as a hobby initially, you wont have wages to pay so $500 (in cash or parts) could be classed as major sponsor (for example). When the series gets to the V8 size, then that is when things start turning pro and the big bucks are required.
This is how I did it mountain biking, I had 2 sponsors at one stage and then moved back to 1 as that was a bike shop that looked after me in racing series. I was not the best rider out there (far from it, they had factory teams anyway), but made appearances at every comp (with banners and apparel) and talked the store up. So remember, sponsorship is not a one way street and it is not as simple as just stickers and paint, you may need to help/provide things in return.
But getting sponsorship is half the fun of the racing (live and breath the sport) and the series sounds exciting. I wish I could be up there to compete, but after the house is built, I will have to organise something down here cause we already have the other good races (MotoGP, Superbikes etc :-). Just wish there was a kart track at Phillip Is.