It should be 'are' if you mean that two things are connected to each other, though it's a bit strange as a pair is usually regarded as a single unit. It would be better to say couple, rather than pair. If you're talking about the pair as a unit, you would use 'is': A pair of pieces is connected to the wall.

#1 is right and #2 is wrong. "Pair" is always singular. #2 is a common mistake. It is an "agreement error". The subject ("pair") and the verb ("is") of a sentence must always agree. The error (no matter what country you live in) in #2 is that the verb "are" does not agree with the (singular) subject "pair". Instead, the verb erroneously agrees with "pieces", which is not the subject.

It always comes down to whether you, the speaker, think of the subject as one thing or two. In many examples of this type, both the singular and plural are natural and correct. There is just a slight difference in meaning or point of view. The couple are divorcing. (The two people) The couple is arriving by car. (The single unit of two people) In your specific examples, however, ‘piece’ is a vague word and ‘pieces’ don’t come in pairs. Both sentences sound wrong and a native speaker wouldn’t say or write either one. Examples of ‘pair’: My pair of 7’s isn’t going to win the hand. (It’s one thing. A unit) My pair of shoes are dirty. (Natural-sounding. Pair of’ here is interpreted to mean ‘two’. However, better and more precise would just be ‘My shoes are dirty’ or ‘Both of my shoes are dirty’. This is because ‘pair’ emphasizes the unit which isn’t the intended meaning.)

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