When is the object of a verb the subject of the gerund in structure "subject + verb + object + preposition + gerund"?

From The Website of Prof. Paul Brians (Washington State University):

Verb forms ending in “-ing” can function as nouns and are sometimes preceded by pronouns. Such verb/noun forms are called “gerunds.” You’ll often see sentences like this: “I didn’t appreciate him returning the car with the gas tank empty.” But “returning” is a gerund, so it should be preceded by a possessive pronoun: “I didn’t appreciate his returning the car. . . .”

Other examples of standard usage: “Their coming to my birthday party was a nice surprise.” “I didn’t like his being rude to his teacher.” “They weeded the garden without our having to tell them to.” “Coming,” “being,” and “having” are all gerunds, and require preceding possessive pronouns (“their,” “his,” and “our”). If a person’s name appears just before the gerund, that too needs to be in the possessive form: “We’re excited about Bob’s winning the tournament.”

As per this, if the OP's sentences are rephrased as follows, the ambiguity can be avoided.

1) This reminds me of my climbing Ben Nevis years ago.

2) I told you about my losing the credit card, didn't I?

I would have to say that this is all about context.

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I failed to find references in major dictionaries, so I would have to quote other less recognized sources:

From The "subject" of the gerund | Grammaring - A guide to English grammar:

The doer of the action expressed by the gerund can be[...]unexpressed and understood only from the context

From Gerunds as Subjects | Grammar Quizzes:

Because a gerund clause is reduced (i.e., not marked for tense, person, or number, and the subject omitted) information must be understood from context.

(I am well aware that the second quote is about gerunds acting as subjects, but I think the two situations are similar enough.)

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My analysis:

1) This reminds me of climbing Ben Nevis years ago.

"Climbing" is an action which only a human (and some animals) can do, and I would assume "this" is something inanimate, so the subject is clearly "I" instead of "this".

2) I told you about losing my credit card, didn't I?

Here, the subject is "I" because in the gerund there is "my credit card". If I phrased it this way, the subject would be "you":

2*) I told you about breaking your knees, didn't I?