Final answer:
The provided texts do not include a character named Sound of Running Feet, nor do they mention a scenario involving the character observing White Settlers mining for gold.
Step-by-step explanation:
Based on the provided excerpts, there does not seem to be a character named Sound of Running Feet, nor any direct mention of the reactions to a White Settler and his wife mining for gold in the stream. The excerpts do not present a narrative that answers the given question.
The provided texts appear to be from different contexts and discuss diversified scenes such as animals in the wild, rustlers moving supplies, and characters experiencing personal revelations and conflicts. Therefore, without additional context or specific reference material where a character named Sound of Running Feet is involved, it is not possible to provide an accurate response to what the character does when seeing someone mining for gold.