Damn, Google pulled the plug on this.
It's all gone on desktop, nothing in the HTML, no popups on browser back button.
Still works on mobile/chrome. I might have a trick to port mobile SERPs over to desktop and scrape the keywords. Don't want to go into details, Google probably has a Google alert and got a hit from this thread, lol.
I'm sure the majority of search traffic will never see the suggested keywords popup because most folks don't hit the browser back button to go back and repeat the same search query. Also opening a Google search result in a new browser tab (Chrome) doesn't trigger the suggested search keywords, even If you go back and refresh the SERPs.
Personally I open search results in new tabs since the invention of multiple browser tabs, it's just easier (IMO).
This also works on mobile (Android/Chrome) and returns extremely GEO located suggested searches.
Example If you search buy house and use a nearby town, not the town you're actually located (ex: buy house [nearby town]), Google will include suggested searches per some ranked organic listings for your exact location/town.
Works the same way, click the ranked page, click the back button on the browser.