Can a site's appearance in the Google Suggest dropdown be manipulated?

A customer has asked this morning why he isn't showing up at all in the "Google Suggest" (I think it's called) dropdown. He complains that one of his competitors开发者_JS百科 is the first ranked result in the Google Suggest dropdown.

The competitor's business name is made up of common words (e.g. Widget Manufacturing) so, sure, he does show up. My customer, whose business name is a proper name, is totally absent from Google Suggest. It concerns him.

How do Google determine what appears in the Google Suggest dropdown? Is it something to worry about in terms of SEO? What would be a good response to the customer?

Update: 2 months later

He now shows up in Google Suggest ... we didn't change anything. I guess it's just Google being Google

Google suggest is just a listing of commonly searched-for terms. The reason "Widget Manufacturing" shows up is because a lot of people search for that exact (or a similar) phrase. Google Suggest has nothing to do with SEO. You could potentially have a very high listing on Google Suggest and have zero results on Google Search (although, that's highly unlikely).

As far as I know, you will have no control over this. No individual websites show up under Google Suggest anyway, just similar keywords. Tell him his competitor is only showing up because his business name is a common keyword, and that his best bet is to try to get in the top of the search results for that keyword, via organic results or PPC.