Great article on KISSmetrics about the length of landing page.

There are lots of analytics tools to learn how your audience treats your landing pages. It differs from subject to subject and is really unique to your product/service, as you may encounter different results than what are "best practices".

We use a combination of Hotjar for heatmaps and recording users, and Heap for detailed event tracking.

I think you'll love what fullstory.com does.

I'd try Hotjar, they will provide both scroll length and the amount of click/movement down the page through heat maps. For further investigation you can use thescreen recordings. Also second Heap Analytics for stronger event-tracking.