The idea that perspective doesn't have any agency is intuitive to Western thinking, but some Eastern philosophies argue in the other direction: Perspective is the source of agency under those ideas.
For me, the Relationship Story is the energy, tension, and dynamic between certain players in the story. Under this guise, the RS is not a character, but has character, an atmosphere that waxes and wanes, ebbs and flows, all of it's own volition. (This volition is key, as there are energy, tension, and dynamics among all players in a story, but only the RS has this volitional feel to it.) When I write my outline, this is what I write about.
Transferring this to storytelling comes by conveying that atmosphere when the player components of the RS are on stage. It's less about the words, and more about the mood, movements, and specific demeanor in deep moments between these players. This is most often done subconsciously, but sometimes there is a zen clarity to what a scene should be, especially for those that need to be pure RS, that I can write about that.
Somewhere on this board, someone said that describing the RS when focused is likely similar to using colors and feelings. I've found that to be surprisingly accurate. Quite often, the strongest word to use for the conflict happening within the RS is a color, or set of colors, or a reference to Feng Shui or something similar to such a conceptual framework. Then, that feeling can be transferred to the storytelling.
That is, unfortunately, the best I can do to explain a practical measure based on how I view the RS. I must admit, though, that I feel like I intuit the MC and RS throughlines rather easily. The IC and OS throughlines give me more trouble, especially the IC, as odd as that may be. I wonder if that could be due to my attempts at understanding East Asian ideologies while in was in middle school...
I wish I could better explain my approach based on my intuition, but that's about all I can say on it so far. My hope is that this at least helps add to the conversation, though.