Hi there,
Your code/process seemed to work out for me in terms of logging the time. The only difference is that I had to add the following code to my JS at the bottom:
Qualtrics.SurveyEngine.addOnUnload(function()
{

timer = clearInterval(); 

});
This is, of course, if "logged to the console" means logged as an embedded data field. Otherwise, be sure to add console.log(timeleft) in various places throughout your code above. For example, I tested with:
Qualtrics.SurveyEngine.addOnload(function()
{
var timeleft = parseInt("${e://Field/TimeLeft})");
console.log(timeleft);


var timer = setInterval(function () {
  if (timeleft <= 0) {
    clearInteval(timer);
    $('NextButton').click();
  }
  timeleft--;
}, 1000);


$('NextButton').onclick = function (event) {
  Qualtrics.SurveyEngine.setEmbeddedData('TimeLeft', timeleft);
  console.log(timeleft); 
}


});
In terms of moving to the end of the block, this code won't automatically do that. Are you trying to do this just for one questions, or over multiple questions?

I’m trying to have the yes/no response recorded in addition to the time. The time has been working fine but the yes/no responses were not being recorded. I have  60 questions that I need the data recorded. I know I will need to adjust the JS for each question and I suspect I will need to add an embed block before each one as well.