Learn English – Difference between seen vs saw

It's I saw you or I see you (if playing hide-and-seek or peek-a-boo).

When you say I have seen you, what you're really saying is I've seen you several times at [possibly] various places. Or that you've just seen them around somewhere or sometime. There is no indication of a beginning and end of the event; or if there is, you're unaware of the details.

Present perfect is used for events that began at an unspecified point in the past. You may or may not know whether it's still happening or not. It usually has relevance to the present,

As for I saw you, that's the simple past; and as you've suggested, it's correct.

The simple past is used for events that have only occurred once, were one-time events with a definite ending, and/or are not happening again (i.e I mean that specific event).

So, to return to the hide-and-seek reference, you use the simple past saw because you only saw them ocne. And once you saw them, that event was over.

Where it gets tricky is that I saw you technically means:

I saw you hiding in [the closet]. So you only say that after they come out of hiding, meaning You weren't very well hidden, because I saw you the entire time.

If they're hiding, and you can see them, then it's obviously I can see you.

I've seen you hiding, means you've seen them hiding previously, possibly many times. It also is something that you would say if your child asked you to play hide and seek; in turn, you'd say:

Please. I don't want to play; there's no sense in playing since every time we do, I've always seen you hiding. It's just too easy; I've beat you several times already.

The best rule of thumb that I can think of would be that if it only occurred once, you have no reason to expect it will return, and you know exactly when it happened, then it's the preterite.

Otherwise, you'd use the present perfect.

This "authority" is in error; the past perfect is not necessarily required here, although there are circumstances in which it would be preferred in formal discourse, and the simple past is not incorrect, although there are circumstances in which its use would be deprecated in formal discourse.

This is in the first instance a matter of context— specifically, what you are trying to express and what time you are talking about, what grammarians call Reference Time.

Perfect constructions do not express events prior to Reference Time; they express a state grounded in prior events which obtains at Reference Time. So if you are talking about a time in the past when your subject's previous unfamiliarity with bears was of immediate relevance, the past perfect will be appropriate:

As she was hiking in the Tongass National Forest she was suddenly confronted by a menacing dark creature her own height and twice her mass. She did not recognize it—she had never seen a bear before she moved to Alaska.

But if your Reference Time, the time you are speaking about, lies before the time at which she moved to Alaska, a past perfect will not be appropriate:

She was in her youth a keen student of wildlife—kangaroos, wallaby, emus—but she never visited zoos, which depressed her, so she never saw a bear before she moved to Alaska.

In less cut-and-dried circumstances, usage varies: formal usage and British colloquial usage tends to employ the past perfect more often than US colloqual usage. If you have an appetite for technical grammar, I modestly recommend our Canonical Post on Perfect Constructions, particularly sections 3.2 and 4. If not, the best 'rule of thumb' respecting use of the past perfect is FumbleFingers‘ Perfect Truism:

”Don’t use the perfect unless you need it.”