I have set up a Content Source that searches our intranet site which is not a SharePoint site. Is there a way to now connect to those search results in SharePoint from that external website? Basically, I want a search box on our non SharePoint site that connects back to the crawl results for that content source in SharePoint. Hope this makes sense.
It's absolutely possible. But it depends on which version of SharePoint you are using.
If it's 2013 or 2016 on premises or online, it's possible.
First you have to crawl external contents from SharePoint search and ensure that your service account that crawls the content has necessary permissions.
Then you can use REST API in your external website that will call the SharePoint site and display the results.