Even though there wasn't a way I could see this, I believe there's a sink hole in the creek bed above the falls. Most of the flow of the creek falls into the sink hole before re-emerging out an apparent "tunnel" opening that I'm claiming to be the thick span of the natural bridge. The visibly thin column of water fronting that opening is the overflow of Running Eagle Creek that managed not to fall into the sink hole. So I'd imagine under lower flow conditions, that extra column might disappear entirely as the rest of the creek would fall mostly unseen before passing through the span of the natural bridge.

The walk to Running Eagle Falls from the large car park was a mostly flat 0.5 miles (one-mile return). The walk was pretty straightforward, and along the way, there was a bench to enjoy the falls with the mountainous backdrop as well as a one-sided footbridge to get you to the viewing deck for a closer look at the falls. I noticed that the trail continued beyond the designated viewing area, but I believe the park closed it because I saw a section of unstable earth as well as a massive rock fall a little further.

It turned out that despite the tranquility of Two Medicine Valley, this waterfall was pretty busy because the old school red tour buses would frequently stop here.