It's not always a question of "either-or." We say
1. That pair of trousers BELONGS to me
"Pair of trousers, pants, shorts, etc," is usually singular, and takes a singular verb. Still, Google search examples include plural verbs. A search for "pair of trousers HAVE/HAS" reveals 80 examples with HAS and 20 with HAVE.
2. A pair of birds SINGS/SING in the garden
Merriam-Webster's Dictionary of English Usage (1994) states:
"Pair is one of those collective nouns that take a singular or plural verb according to notional agreement. If you are thinking of the individuals in the pair, you will use a plural verb:
"A pair of elephants were grazing near the camp ...
'If you are thinking of the pair as a unit, you will use the singular:
"Genuine crocodile loafers....the handsome pair has a hand-sewn moccasin construction...."
With the noun "birds," however, the results on Google are about 50-50. Google examples:
"” A mourning dove can be obtained as a chick from bird breeders. When a pair of birds are placed together they stay for life together for breeding.
"” Birds are free-fed for several days and once trust is established, they are easily caught. Sometimes a pair of birds are placed in the trap to lure others in
"” This second pair of birds has reared three young, having been established in their cliff top home by Operation Chough, at Paradise Park in Hayle.
"” Everyone wants to know what their pair of birds is capable of producing. If the breeder doesn't know what to pair with what, the results can be disappointing.
3. The couple LIVE/LIVES next door
Neither LIVE nor LIVES is completely wrong, although the preferred verb number is the plural, LIVE.
With "couple" a Google search finds far more plural verbs than singular (five to ten times more). Also, according to Garner,*
"When two people form a couple, they may act as individuals <the couple plan to take jobs in Philadelphia> or as a single entity <the couple is buying a house>. But unlike other collective nouns, couple should take a plural verb far more often than a singular one."
My own Google search turned up a wide disparity between the two strings "by the couple who have" and "by the couple who has." "Have" is found in 65 examples, while "has" occurs in 6.
*Garner, Bryan A., Garner's Modern American Usage (Oxford University Press, 2003)