Here is my view of the relationship of the functions:
Thinking and Feeling:
I believe that any chain of logic, however long, that a decision is based on, if followed back, starts with at least one emotional value. Emotions set the goals. Logic decides how to reach them.
Thinkers assign these emotional values subconsciously, then consciously go through a chain of logic. The chain of logic can go far enough away from the original emotional values that it gives the illusion of pure logic.
To see how this works, take any decision you have made. Why did you decide that way? Now take that motivation. Why did you want that? Keep following it back far enough and you will get to something emotionally based.
Feelers consciously feel emotional values, then go through a subconscious, and shorter, chain of logic to assign emotional values to other things.
iNtuition and Sensing:
iNtuition and sensing have a relationship similar to that of thinking and feeling. All chains of intuition start with a sensory input of some sort.
iNtuitives subconsciously take in a bit of sensory input, then consciously go through a chain of intuition. The chain of intuition can take such big leaps and get so far from the original sensory input, that it becomes totally unrelated. This can give the illusion of pure intuition.
There have been a number of times where I, as an intuitive, have been thinking about some random topic and thought to myself "How did I get on that topic?" Unfailingly, when I trace my thought process back, I get to a sensory input.
Sensors consciously take in sensory input, then follow a subconscious, and shorter, chain of intuition.