I just tested the "Google Custom Search" on my site.
70% of search results showed the sprite left of the text listing.
Ah, I see. Yes, Google Custom Search likes to show thumbnail images, so they need something to show on the left side. Forgive length of this in advance...
It may be that if your logos, say, are all on your Sprite Sheet, Google's image algo might feel that the best thumbnail choice it has is the entire sheet. There would be a lot of factors affecting this, including what other choices there are.
What you need, IMO, is a way of specifying something analogous to a Facebook Open Graph image in your head section, in which you are able choose an image to display when a page url is called.
I don't think that Google has anything that's precisely the same, but there may be something you can do involving proper schema markup, as described in the Google Developers Structured Data documentation, which is similar.
To see what we've discussed here before, involving both Google markup and also how Google might choose its thumbnails if it does so algorithmically, I'm listing several prior threads and where they lead. I suggest you follow them backwards and maybe do some testing.
A question also about images in Custom Search came up a few years ago... Google site search: customizing with rich snippets Jan 2, 2014 https://www.webmasterworld.com/google/4634966.htm
While the discussion fizzled, and we don't know whether it was followed up, I think the answer probably is in the thread I recommended about how Google might choose images for thumbnails in Food Recipe searches. Food Recipe SERPs and Thumbnail Photos May, 2013 https://www.webmasterworld.com/google/4574582.htm
tedster there suggested checking out Google's Rich Snippers markup documentation. Google Developers - Structured Data Rich Snippets for Recipes
Note that in this section of Google Developers documentation, Google also discusses many rich snippets areas beyond recipes, including Products, Reviews, Music, Books, etc, etc.
Essentially, I think you'll have to provide for Google an image that's an alternative to your Sprite Sheet, and either to mark it up in a way that Google will use it in Custom Search, or to make it distinctive enough in a visual way that Google might algorithmically use it.
I'd be very interested in what works if you try it... or in any other approaches people have tried that might work.