I build a lot of tools like that and the first thing I do is to go to the developer tool in my browser and observe the network traffic. When you find the resource you’re after you scroll back and see what requests resulted in that URL. Going from those requests you figure out in the original static HTML document and resource, which parameters are used for the construction of the URL, that might require reversing some javascript, but that’s rare. After that you’ll have a pretty good idea how you obtain the video resource from the original URL. Beware of cookie set by the requests, they might be needed to access the next requests. For building my tools I use Perl or sometimes just Bash or a GreaseMonkey userscript to fetch and parse the urls and construct the desired output.
Kekin