I have collected 6 research studies on visitor eye tracking and done the studying for you. Here is what eye tracking studies talk about conversion rate optimization:
F-Shaped Pattern For Reading Web Content – the most well known article that laid out the generally proved F pattern of attention on a webpage. The pattern suggests that headline and starting paragraph are THE most important elements on your page.
More complex your page is, more the possibility that the visitor will take an unexpected eye gazing path on your page (which may reduce the chances of missing your call to action).
The first page the visitor lands on provides a lot of context to his total browsing experience on the site. What he may miss on the first page, may be not be noticeable during his total further interaction on the website.