The advice to dance as if no one were watching works for shy people and extroverted showoffs as well.
If you are shy, worrying about what people think, will take away from your focus on your partner and the joy that you could be having by dancing only to the music. Sure, you may enjoy the moment of communal joy with others on the dance floor, but my ideal is to dance among other as if no one were watching. Two hearts are moving in harmony and remaining centered on each other.
If you love putting on a show, I believe these words of advice are especially for you. I am not pointing any fingers. I am both shy and have elements of loving to be on stage (the youngest of 7). I have played in front of thousands as a musician.
BUT TANGO has changed me. When I first started out, I almost immediately was enjoying praise at dance parties with Alicia, my tango coach in El Paso. (This does not mean I was any good.) But then one day, I realized that the only person who mattered was my partner. Worrying about others (or hoping they are watching) takes away from what is important. I learned this in Austin with Stephen and Mardi Shortancy more than anyone else.
I started dancing like no one was watching. And I wanted it to be my standard.
Shortly thereafter, a woman who had seen me dance told me after our first dance of the tanda, "I wished I had known you dance like this... one can never tell if the person who looks good, feels good." So true. Many are drawn to tango for the way it looks, but only those who fall in love with the feel of tango stay with it. Even teachers who focus on "looks" will burn out. If you can teach someone to feel tango, then it is soul work, not feeding an insatiable ego interested on added on more impressive steps. People like Austin's Alicia and Juan Carlos (from Buenos Aires) are like this. They are so in love with each other and have worked for so many years teaching because of the feel of tango.
So my challenge is that you look at the people who have been doing tango for decades. I think they know better than anyone how to dance like no one is watching. In this video (Pocho and Nellie at El Beso), pay attention how Pocho often places Nellie's foot and has her lead through the music. I think they are totally lost in the music and each other. Others are watching but I don't think they are even aware in their moments together.
Sing as if no one is listening and dance as if no one is watching. It's good for the soul.