Check out the geolocation sample for an example of how to do this with CSS3: http://help.arcgis.com/en/webapi/javascript/arcgis/help/jssamples/exp_geolocate.html
Just a side note. We had a blinking location on our maps. The overwhelming comment was
"How do i turn the &()&*(^_(^ heartbeat off"
People, overwhelmingly , HATED it.
I'm happy to hear this. Animation for animation's sake usually isn't a good idea. Unless you have customers who absolutely demand it, you probably shouldn't do animated/pulsing map symbols.