Are you in North America?
Please note that the term "Component" could lead to confusion as it can mean both "RGB" and Colour Difference Video (YCbCr).
In which case, there are two different beast...

Any north american television with "Component" input are most likely referring to Colour Difference video.

I've looked around for a means to convert RGB (what amiga generates) to Component Video, but haven't had much luck. I've seen something that does the reverse (converts YCbCr into RGB) for around 175$US.