I don't think the rank of the co-author list is random. It must follow some order that's definitely not the time order. I used to think that this rank depends on the number of papers you and the co-authors wrote, the number of citation of those co-authored papers have, etc. But I don't think this is true now since I found some hard evidence that this thought failed. So my question is how Google Scholar ranks the co-author list?
The coauthors are ranked by relevance, and the exact definition of relevance probably changes over time. Papers and citations are obviously important factors. Google may also consider other factors such as the age (or age distribution) of the citations or the overall ranking of the coauthor among all researchers. The ranking of A in the coauthor list of B might also be influenced by the ranking of B in the coauthor list of A.
In my profile, a coauthor with 2 shared papers (20+3 citations) is ranked higher than a coauthor with 3 shared papers (9+3+0 citations). This person is ranked higher than another coauthor with 1 shared paper (35 citations), who is in turn ranked higher than another person with 2 shared papers (5+3 citations). You could produce a ranking like this with a weighted sum of the number of papers and the number of citations, but that's probably not the whole story.
It's good to remember that Google is a search/advertising company. Ranking pieces of information by relevance is their core business. They won't disclose the exact details of the rankings, as those details are important trade secrets. Google also keeps changing the details, as advertisers and websites would otherwise learn to game the system, making the rankings less useful.