First try to connect the thing without an RF switch. Go back to radio shack and buy the following part:
Female RCA to F-59 Male connector
http://www.radioshack.com/product.asp?catalog%5Fname=CTLG&product%5Fid=278-255 (Actually go somewhere else and pay $1.99 for it instead of $4.99).
Plug this directly into the end of the video cable from the Stunt Cycle and the other end to the coax input on your TV.
See if this improves your picture.
If not, then the cable could be at fault. Crack the case and I think if it's like the 2600, the cable is a male-to-male RCA type, so you could just pop in temporarily a RCA patchcable from a VCR. Try that and see if it improves.
If not, then the last thing to look for is going to be a variable capacitor. They look like a square metal box with a black or painted dial in the center of it. This is made of ferrite (a very fragile metal, almost like cermaic). Take a NON METALIC device, like a cut and trimmed plastic knife and gently turn it one way or another and see if it improves the reception on you TV. If you use a metalic device you run the risk of breaking the ferrite AND it also affects the electrical capabilities of it while you are turning it so if you adjust it and pull a metal screwdriver away it will go out of adjustment... a real pain.
I havn't cracked mine open in ages, so I forget where things are located, plus mine is too burried to dig out right now. Hope this info helps.