Positive or negative private key of a bitcoin wallet?
There really isn't a "positive" or "negative" for private keys. Private keys are unsigned integers, so they're basically all "positive". Your "negative" numbers are not actually negative, they're the modular additive inverse of the "positive" private key.

Since private keys are really unsigned integers, you can't glean any information about signed-ness from the public key because there are no signs to even look at. Every private key is the "negative" of another private key, so a private key is both "positive" and "negative". Every private key has an additive inverse.

However, given two public keys, you can determine whether their private keys are additive inverses of each other by checking whether the X coordinates are the same. If so, one should have a Y coordinate that is odd, and the other have a Y coordinate that is even. This only tells you that their private keys are additive inverses of each other. But you won't know which is the lower number or what one of them is (unless you have the private key for one of them).