As a competitive partner dancer, I too will close my eyes sometimes to shut out distractions and focus on the movement more. This is especially useful while practicing but I also sometimes do it during social dancing (provided there is enough room and I won't be putting my partner at risk by crashing into other people or being crashed into).
Feel the damn music :/
Closing my eyes really helped with removing all stimuli that distracted me from actually doing that and it made all the difference.