I agree. I have all of my students sing the notes out loud of the open strings. While some are more than willing than others to comply (LOL!), it really helps develop a great relationship between the ears and the instrument. Sing everything you play! Literally! You don't have to be a great singer by any stretch, however; this will undoubtedly help you develop the relationship much better.
And also; don't over think it (as mentioned before.) Simply sing with your instrument and be patient, as the progress will happen. If you try and force it your analytical sense will get in the way. Like I said, we all share the same notes my friend.