gerunds - going + ing vs going + infinitive, when use which?

In the middle of a conversation I should use which of the follow sentences:

Tomorrow, I'm going climbing.

or

Tomorrow, I'm going to climb.

I did a deep search and I found these similar answers, 1, 2, 3, 4, 5, 6, 7 , 8, 9. But none of them answer my question.

Also I know that there are three simple rules to use the gerund:

1. After certain verbs


2. When the word is the subject of a sentence or clause


3. Is used after a preposition

My point of view is:

We use to climb doing reference to the action itself. That I'm going to do that action and it's all. However, climbing is when you are referencing the process like naming the process. So, if you are naming the process, is because you are going to tell something about it, something collateral about some phase(s) of the process instead of just talking about the action.

For me, talking about process (-ing), is making a emphasize on time or phase(s) of that process. Am I correct?

Please, I would enjoy and prefer an answer that doesn't say that is how we use or is more common. Because, common action doesn't make it a correct action.

So, phrases like:

If this sounds confusing, just remember that 90% of the time, you will use a gerund as the subject or complement of a sentence.

will not help for me. Just logical answer about the verb or situation or...