To establish a variable as false and trigger a click event on the drop-down menu, simply set up a callback to change that variable to true when the click event occurs. Then, in the blur event callback, include a condition to verify if the variable is indeed set to true.
If you prefer not having to click outside of the drop-down menu after making a selection, consider implementing a mouseout event as well.
let dateSelect = document.querySelector('[name="dayCount"]');
let clicked = false;
function changeClick(){
clicked = true;
}
function checkFocus(){
clicked === true ? console.log('BLUR FIRED -> select has lost focus') : null;
}
function mouseOut(){
clicked === true ? console.log('MOUSEOUT FIRED -> Your mouse is not over the select element') : null;
}
dateSelect.addEventListener('click', changeClick);
dateSelect.addEventListener('blur', checkFocus);
dateSelect.addEventListener('mouseout', mouseOut);
<select name="dayCount">
<option >op1</option>
<option >op2</option>
<option>op3</option>
</select>