Start from what you do now
Pull your last month of response times in business hours. Note the median and the 90th percentile. Your target should sit just outside the 90th: you want to meet it on nearly every ticket and have a little room to improve.
Two targets are enough
A first reply target (how fast a person answers) and a resolution target (how fast it is solved). Add a next reply target later if customers complain about gaps in long threads. More than three targets and nobody remembers which applies.
Vary by priority, not by customer mood
Use priority levels rather than who shouted loudest. The priority matrix turns impact and urgency into P1 to P5. An example for P1 might be a first reply in 1 business hour and resolution in 4; for P3 a first reply in 4 and resolution in 24. They are examples, so set yours from your own numbers.
Count only business hours, and skip holidays
The clock runs only while you are open. List your holidays so they are skipped. A ticket that arrives Friday at 4pm with a 4-hour target and 9 to 5 hours is due Monday at noon.
Pause for the customer
Resolution clocks should pause while a ticket waits on the customer, because you cannot move it forward. First reply clocks do not pause: nobody has replied yet.
Make misses visible early
A target is only useful if the team sees it coming. Show the time left on each ticket, flag the ones near their limit, and alert a lead before a ticket breaches, not after.
Report attainment, then look at the misses
Attainment is the share of tickets that met the target: 480 tickets with 18 misses is 96.25%. Whatever the number, read the misses. If they cluster at 4:30pm, it is a staffing gap; if they cluster on one topic, it is a knowledge gap.