The challenge in your request, is that Javascript does not actually trigger an event when the mouse is NOT moved.
What you need to do is create a timer that triggers after 500ms, and reset it each time that the mouse is moved.
I would use a custom input in order to do this, following is an example of how this can be done.
{
      input: [
        { on: 'click', handle: 'end' ,stimHandle:'clickButton'},
        {
          handle: 'nomove',
          delay: 500, // set length of delay before warning
          on: function(inputObj, canvas, stream){
            var $listener = stream();
            var timeoutID;
            document.addEventListener('mousemove', onmove);
            onmove();
            $listener.end.map(function(){
              clearTimeout(timeoutID);
              document.removeEventListener('mousemove',onmove);
            });
            return $listener;
            function onmove(e){
              clearTimeout(timeoutID);
              timeoutID = setTimeout(function(){
                $listener(e);
                onmove(); // reset the timer
              }, inputObj.delay);
            }
          }
        }
      ],
      interactions: [
        {
          conditions: [{ type: 'begin'}],
          actions: [{ type: 'showStim', handle: 'clickButton' }]
        },
        {
          conditions: [{ type: 'inputEquals', value: 'nomove' }],
          actions: [
            { type:'showStim', handle: 'warning'},
            { type:'removeInput', handle: 'hideWarning'}, // prevent blinkingÂ
            { type: 'trigger', handle: 'hideWarning', duration: 600 }
          ]
        },
        {
          conditions: [{ type: 'inputEquals', value: 'hideWarning'}],
          actions: [{ type: 'hideStim', handle: 'warning' }]
        },
        {
          conditions: [{ type: 'inputEquals', value: 'end' }],
          actions: [{type:'log'}, { type: 'endTrial' }]
        }
      ],
      stimuli: [
        { handle: 'clickButton', media: 'Click me!' },
        { handle: 'warning', media: 'Please move the mouse' , location: {bottom:20}, css: {color:'red'}}
      ]
    }