Have you ever had a speaker ask you to do that? I love looking around to see how many people are “peeking” or just looking at their laps.
When you ask the audience to shut their eyes you are asking them to have an extreme amount of trust in you. You better be sure you have earned that trust or you will really put people off. The other day I ordered a sandwich on French bread. The sandwich man took out the bread, started to cut it and then tossed it out. He looked at me and said, “If I wouldn’t eat it I don’t serve it. The bread is too hard. Would you like to make another choice?” I loved it!
He built trust by being straightforward; he didn’t bash his company and he gave me an option.
Whatever you ask your audience to do make sure you would be willing to do it if you were a shy person or a skeptical person. Those are your two toughest audiences. Build trust with your audience by being vulnerable yourself.