I was recently at the Kotel during Erev Shabbat, and I saw that while most people were facing toward the wall, a few were facing away from it, toward the entrance ramp, and fervently praying in that direction. They were not standing alone, but amongst a minyan in which most other people were facing toward the wall. (And no, it wasn't just at the end of Lecha Dodi, it was for most of Maariv.) I know that outward appearance is not a good way to tell, but they looked like religious Jews to me. Why were they doing this?