Was searching on gaze avoidance and found this one ...
And yeah, it is old ...
http://www.blackwell-synergy.com/doi/abs/10.1111/j.1468-2958 .1979.tb00625.x
Eye gaze avoidance is examined in relation to the occurrence of turn-taking, vocalized pauses, sentence changes, repetitions, "you know," "like," sentence fragments, simple sentences, and complex sentences. The results provide support for the hypothesis that people avoid eye gaze when experiencing difficulty in encoding. This finding is discussed in relation to previous research and possible implications for the study of interpersonal communication.
It doesn't look like the study specifically involved autistics, so I guess you could say there is a natural tendency for all people to look down or look away when they're trying to figure out how to say what they want to say (that's how I interpret "experiencing difficulty in encoding"). Autistics tend to have more problems encoding (and decoding for that matter) so they're naturally also going to have more problems maintaining eye contact. That makes a lot of sense.
Thanks for sharing the link.