eDicky

Your second photo looks like the northbound side of the highway (Vipavadi Rangsit), there's even a tree. If you want to head north you can cross the walkway and go down somewhere, there should be plenty of taxis.

But the southbound frontage road and stairs down that I refer to can be found before you start crossing the walkway towards the rail station and Amari Airport hotel. I'm not sure if it's the one in your first photo, it may be a lane closer in to the airport building under the apron.

The last time I used it a couple of years ago, it was not possible to get hold of a taxi dropping off at the departures level (I think because of so many people desperately trying to escape the main queue), so we went up to the walkway and down to where a line of several taxis were ready and waiting. My daughter and others have done this several times since.