I've heard that while making the ברכה for his aliyah, the עולה should make it a point to not be looking at the ספר תורה but should be looking to the left. Where is the source for this?
There is a concern that the congregation might come to think that the Brachos said before Torah reading are written in the Torah, but closing the Torah and then opening it would take extra time (see Megillah 31a). Therefore, the Rama (139:6) writes that it is best to turn one's head away from the Torah while making the Beracha. Once one is turning his head, it's better to turn to the left, which is the right of the Torah/"shekhina" which is opposite him.
However, the Mishnah Berura (there) notes that several poskim believe that it is disrespectful to turn one's face away from the Torah when he is standing in front of it, and he prefers the practice of closing one's eyes (despite the fact that it may be less obvious to the congregation that one isn't reading the Berachos from the Torah). Many Mizrahi communities have the custom to cover the Torah with a cloth while making the bracha, and this is the suggestion given by the Kaf Hahaim (139:23)