Your analogy about brinks is good to a point. Speaking from experience, building relationships is far more complicated. I would break it down to several steps.

1. Attraction:
   I have witnessed my friends just wink at women at a bar or in a restaurant and women would get up from their seat to share their phone number without a single word. Without physical, intellectual, financial, pheromones attraction there's no interaction.
   Key note=Everything is for Sale and there's a buyer for everything.

2. Courtship:
   After attraction stage, if you to prove that you are worthy their time by showing that you are capable of satisfying her needs. Ex. Sexual, intellectual, stability, etc..
   (Key note= Everybody have needs)

3. Short Relationship:
   After being successful on the first two, you are now in a short relationship (how short?) depends on how long you can satisfy each other needs (stability, sexual, companionship, etc.) and often the happy medium is compromise. Ex. You support this family in exchange I will (A. give you sex B. Raise the children C. Cook and clean D. Etc). If you keep yourself in shape and interesting there's less chances that I will cheat on you or leave you. (Key note= Humans are not and never meant to be monogamous)

4. Long Term relationship:
   Often after the basic needs have been covered. There's only a friendship keeping the relationship afloat. By basic needs I'm referring to: A. Show my parents and/or society that I'm an adult. B. Children can walk and eat (7 years itch). C. financially stable. D. I'm sexually satisfied. (Key note=XXXXX) Fill the blank...

sometimes though you instantly click

I am currently building a relationship, I think. We have known each other for about 5 years and hardly paid any attention to each other for most of it. But as we have Slowly gotten better acquainted, we find ourselves having the Best time together regardless of what we are doing. We both have had some tough times in our lives (I am 69, he is 73) and are equally not sure if we want to be opening up this particular can...but, wow, do we have fun together!
I have also experienced several relationships where only one of us "felt the spark". Very painful!
I have also gotten into a relationship or 2 where that "-spark" led me Far astray from what was good for me!
So I am Extremely wary of that "spark" thingy! Use the brain!

This is a great analogy for some people, but I imagine personality and experience have a lot to do with it. Certain personalities are more guarded, and some are a lot more trusting (too trusting, some of my friends confound me with how poorly they're able to recognize red flags in another person). Past experiences have a lot to do with it, as well. Some people have been lucky enough in relationships they don't feel the need for some large wall when meeting people, but I don't think that applies to many of us...

Some folk simply click...

You are correct. In order to form a close relationship, one must be willing to allow oneself to be vulnerable. When that vulnerability is reciprocated, a real basis for a relationship exists.