Does the hand-held mobile phone ban apply while queueing in Northern Ireland traffic?

Yes. Being stationary in a queue or stopped at traffic lights does not remove the hand-held phone restriction.

nidirect specifically identifies queueing traffic and traffic lights as situations where a driver must not hold and use a phone. The exemption for a genuine emergency call to 999 or 112 is narrow and requires that stopping safely would be unsafe or impracticable. If you need to text, change navigation or answer a call, park in a lawful place first.