Вы можете сохранить фактические значения на карте, передать ключ для карты, которую вы хотите настроить, и ссылаться на нее.
const elemHoursIncreaseBtn = document.querySelector('.hours__increase__btn');
const elemHoursCount = document.querySelector('.hours__count');
const units = {
hours: 0,
minutes: 0,
seconds: 0
};
function increaseCount(unitType, number, elem){
if(units[unitType]<number){
units[unitType]++;
if(String(units[unitType]).length<2){
elem.textContent = "0" + units[unitType];
}else{
elem.textContent = unit;
}
}else{
units[unitType]=0;
elem.textContent = "0" + unit;
}
}
elemHoursIncreaseBtn.addEventListener('click', function(){
increaseCount('hours', 23, elemHoursCount);
});
.flex__center{
display: flex;
flex-direction: column;
justify-content: center;
}
.timer__container{
display: flex;
flex-direction: row;
}
.increase__pick, .decrease__pick, .hours__count, .minutes__count, .seconds__count{
text-align: center;
}
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<meta http-equiv="X-UA-Compatible" content="ie=edge">
<title>Timer</title>
<link rel="stylesheet" href="../css/timer.css">
</head>
<body>
<div class="timer__container">
<div class="hours__picker">
<button class="increase__pick hours__increase__btn">/\</button>
<p class="hours__count">00</p>
<button class="decrease__pick hours__decrease__btn">\/</button>
</div>
</div>
<script src="../js/timer.js"></script>
</body>
</html>