Running a jQuery function multiple times sequentially (for a Bookmarklet)

Try it this way (using ES6 Promises):

var runUnfollow = function() {
  return new Promise(function(resolve, reject){
    var index = unfollowButtons.length - 1;

    // fencepost for the loop
    var p = Promise.resolve();

    // we stop execution at `i == 0`
    for (var i = index; i >= 0; i--) {
      // run the promise
      // then set `p` as the next one
      p = p.then(unfollowTimeout.bind(null, i));
    }
    // make sure we run the last execution at `i == 0`.
    p.then(function(){
      resolve();
    })

    function unfollowTimeout(i){
      // return a promise to run `unfollow` and a `setTimeout`
      return new Promise(function(resolve,reject){
         unfollow(i);
         setTimeout(resolve, Math.floor((Math.random() * 1000) + 500));
      })
    }
    function unfollow(i) {
      $(unfollowButtons[i])
        .click();
    }
  })
}

// run three times synchronously
runUnfollow().then(runUnfollow).then(runUnfollow).then(function(){
  //finished
});

// another way to run three times synchronously
p = runUnfollow();
for(i=3; i > 0; i--){
  p = p.then(runUnfollow);
}
p.then(function(){
  //finished
});

// run in parallel
Promise.all([runUnfollow, runUnfollow, runUnfollow])
  .then(function(){
    //finished
  });

EDIT: Went back and read your question again, realized you were trying to run everything multiple times. I've edited to reflect that.

Just reset index and restart after each button is clicked:

javascript: (function() {
    var unfollowButtons = $('button.Unfollow');
    var index = unfollowButtons.length - 1;
    var totalRuns = 3;
    unfollow();

    function unfollow() {
        if (index < 0 && totalRuns) {
            totalRuns--;
            unfollowButtons = $('button.Unfollow');
            index = unfollowButtons.length - 1;
        }

        if (index >= 0) {
            $(unfollowButtons[index--])
                .click();
            setTimeout(unfollow, Math.floor((Math.random() * 1000) + 500));
        }
    }
})();