I sense something fishy from your flattery, but whatever.
I doubt I can fully answer this question, for I asked the same question years ago.
The answer I was given at the time was that there's no definite line drawn between these two tenses but the difference is that the past tense seals the deal for good whereas the present perfect, rather than "you were doing something and you are continuing that action" as you said, leaves open the possibility of different actions at the point of speech.
(I'm referring mostly to
this thread - see ricardosong and Tdol's explanation on present perfect and the past tense)
I myself would not have been able to answer the question on the spot. But I've given some thoughts and I think this is how I would answer the question. I was pleasently surprized to see myself duducing a lot of ideas from the above explanation.
Regarding your quesiton on why "I have been looking for you," I think it's emphasizing the duration of time between past and present.
What I'm saying is, if you drew a horizontal line to represent time, "have been looking for" would look like a line from a certain point in the past to the present, whereas "was looking for" would look more like a dot in the past describing just that point in time.
That's why you can append extra information, such as when the action was started, to the present perfect form. Like this: I have been looking for you since noon. If you spoke the sentence at 7 in the evening, you are making the connection from noon to the present (7pm), thereby emphasizing that duration. On the same token, if you say "I've been looking for you since we parted our ways 20 years ago," you're saying your search started 20 years ago when we parted our ways and has been an ongoing thing until now. This connects the past and present.
In the case of "I was looking for you," however, there's no connection established between the time of action (past) and the point at which you're speaking the sentence (present). If you add extra information and say "I was looking for you 20 years ago," you are saying you were looking for me 20 years ago but have since stopped the search, showing no connection between 20 years ago (past) and when you're speaking the sentence (present)
And because in the sentence "I have been looking for you" the person the sentence is spoken to and the object of the search are identical, this makes explaining the 'undecided future' aspect of the present perfect tense difficult. Try replacing 'you' with any 3rd person who's not in the conversation (him, her, Jimmy, mike, that creepy guy we met at the party and so on) and you will better understand what I meant in the beginning by "leaving open the possbility of different actions"
If you say "I have been looking for him," it means you have started the search from an unspecified point in the past (which you can specify by appending "since..."), you haven't stopped the search up until the very moment your speaking the sentence, and from that point on you 'may or may not' continue looking, because you haven't found him (provided 'he' is not in the conversation).
This funciton of possibility in present perfect, when the object of search becomes 'you' that you're talking to, becomes obsolete, because when 'you' are right in your face, why continue searching? This way, only the function of establishing the connection between past and present is retained. (is what my theory is. If I'm wrong, oh well)
Ok, "looking for" may not be the optimal verb for explaning this concept, because...
- From here on it could get a bit confusing. If my explanation so far was overwhelming enough, skip this part. You should be OK bro, but it might be too difficult for your friend -
...because "looking for / found" works in pairs.
In fact, "I was looking for you" works just fine in your situation, because "and now I've found you" part is omitted. Obviously, when I say this sentence to you, I've found you. You're there. And it's grammatically incorrect to say "I've been finding you," hence the looking for / found pair. Since the omitted part, "I've found you," is already present perfect and connects past to the present, it doesn't matter whether the sentnece before that is simple past or present perfect.
- The confusing part ends here.
Let's try another verb. Just 'be'.
You were mine. (but not now)
You have been mine. (affirming the ownership from one point in the past until the moment the sentence is spoken)
Whatever may happen after has not been mentioned and becomes a possibility with different futures. It's not "continuing the action from the past" as you said. Continuing the ownership may be a possible future, but before the next sentence it's possible neither to affirm or deny it, thus no conclusion can be drawn. It could either be "You have always been mine, but now I'll let you go," or "You have been mine, and you will always be," but before the next sentence, what's only certain is the period from the past to the present and the future hasn't been mentioned yet.
This tense doesn't exist in Korean and that makes it especially hard to explain. My theory is still in a development stage. I'll come up with something more later on. Hope this helps.
- your brother