Is pair followed by singular or plural? What about adding a noun directly after pair

Is pair followed by singular or plural? What about adding a noun directly after pair

Pair itself can be singular or plural. But the noun after pair of must be plural: a pair of shoes
Even a pair of pliers;
A pair of black trousers
If it is an attributive phrase, according to the rules, the noun should be singular:
Pair Card Game
The system is modeled by the Hartree-Fock description of a pair electron interaction.
If it is a noun phrase, the singular and plural should be determined according to the emphasis of the sentence
The player places a base pair card from his hand into the sequence.
In case when a winning combination or a pair cards are drawn,these cards will be held automatically.
Lone pair electrons have a stronger repulsion than bonding pair electrons.