In order to answer your question properly I feel we need to focus on the sheer base of it, which you so kindly placed in bold.
Even though it is difficult to make "acts of patience" the basis of a story, what if that's what we want to do? Indeed, how might we make "acts of patience" exciting?
Now, my answer comes in two parts. Defining the Act & Executing the Act
Defining the act
Acts of patience have a variety of implications for story telling and some are inherently easier to "spice up" than others. These can be defined by either an act that will be resolved in the immediate to near future, and acts that are "playing the long game".
Short-term acts could be things like a hunter mentally ramping up and talking through the act of pulling the trigger.
As he approached the top of the rise, John crouched and lowered himself slowly and began to crawl through the tall grass. His knees wet from the dampness of the morning dew, he pressed forward to the top and pointed his rifle down hill - where he knew there would be a small group of white-tail deer waiting for him. He checked his watch, there was still two minutes before legal light, two minutes to do all he must and wait before pulling the trigger. One hand still on his rifle he grabbed his binoculars from his chest pocket and looked through the herd, one buck stood out against the rest. It was magnificent, his antlers cropping up and out beautifully gracing his head like a crown. He sighed, checking his watch again, as the wind shifted now blowing his scent directly into the herd.
One more minute.
The kingly buck's ears perked up as he looked around, John's scent filling his nostrils. John knew it was only a moment before the buck would turn, lift tail and run.
John shift his position and lifted his rifle into position and counted down, time seemed to stand still - each second longer than the last. He rested his sights on that little spot just between the ribs, where he knew his bullet wound puncture both lungs and the majestic animal's heart, a quick and humane kill. Five. The buck shifted, still smelling the air. Four. John nervously shifts his aim to match. Three. His finger curls around the trigger. Two. The buck looks straight at him. One. He holds his breath to stabilize his shot...Zero. Bang...he pulls the trigger.
As we read through this example, John displays enormous amounts of patience in the act to get his buck. However, as a reader (and being a hunter myself) I can place myself in his shoes. Patience, even in real life, can be exciting.
While longer-term acts need to have an end goal and aim in mind - even if it isn't immediately apparent to the reader. For instance, your example with Sansa Stark shows the exact opposite. Martin portrays her as a "little bird" initially, and that innocent trait is picked up by The Hound, who affectionately (off and on) calls her that throughout their interactions. She goes from being a timid, quiet and proper young woman to ,what some would call, a brilliant tactician who learned from her woefully miserable past. However what Martin did was build her up slowly - starting with the death/unjust execution of her father. She sought to free herself from the wills of others, seeking out partnerships or lessons from those she deemed smarter/worthy of her (Lady Martyl - spelling, Little Finger, her aunt in the Vale, etc.) Please forgive the spelling or lack thereof...Martin had a way with names.
All that said, her acts of patience while slow in development from the reader's view, were frequently exciting and clearly building to something (even if you didn't read the books, which I recommend, the show captured this as well). As a reader, I didn't feel forced or bored reading her timeline - even though for the most part it was less slashy/sexy/adventury than the others.
Executing the Act
Writing like anything that is creative or requires something to be built needs to have an excellent foundation in order to be effective. In this case, your foundation would be your plan - what gets accomplished by this portrayal of patience? What do we as readers take from it? What is gained by this for the character in this event?
There needs to be a reason. Human beings, most creatures for that matter, are relatively lazy and selfish we generally don't do anything unless we feel we need to and get something from it (even that "warm feeling" from helping someone is getting something for simplicity's sake).
So in order to execute this effectively you need to have a clear idea of what you want accomplished, a clearer goal for your character and solid story arc to balance this exercise out to give the reader the resolution they deserve.
Hope this helps!