In the sentence

• The player appears to have not connected.

connected is the focus of negation, and thus not can appear directly before it, as here.

However, not can also appear directly before the beginning of any constituent containing its focus.

Connected is in the Verb Phrase have connected, so not can go before that, too

• The player appears to not have connected.

and also in the Infinitive Complement to have connected, so not can go before that, too

• The player appears not to have connected.

Since appear is a Neg-Raising verb (i.e, it's transparent to negation), not can also negate
the complex VP constituent appears to have been connected.

This, of course, requires Do-Support, because appears is present tense, and negating a tensed verb
requires an auxiliary verb to carry the tense. When there's no auxiliary verb already in the tensed VP to be negated, one uses Do. That's Do-Support; i.e,

• The player does not appear to have connected,
  or, more likely
• The player doesn't appear to have connected.

They're all grammatical, and they all mean the same thing.
And I didn't even mention A-Raising.

In the sentence

• The player appears to have not connected.

connected is the focus of negation, and thus not can appear directly before it, as here.

However, not can also appear directly before the beginning of any constituent containing its focus.

Connected is in the Verb Phrase have connected, so not can go before that, too

• The player appears to not have connected.

and also in the Infinitive Complement to have connected, so not can go before that, too

• The player appears not to have connected.

Since appear is a Neg-Raising verb (i.e, it's transparent to negation), not can also negate
the complex VP constituent appears to have been connected.

This, of course, requires Do-Support, because appears is present tense, and negating a tensed verb
requires an auxiliary verb to carry the tense. When there's no auxiliary verb already in the tensed VP to be negated, one uses Do. That's Do-Support; i.e,

• The player does not appear to have connected,
  or, more likely
• The player doesn't appear to have connected.

They're all grammatical, and they all mean the same thing.
And I didn't even mention A-Raising.