I noticed this happening in my blog's logs months ago, for my blog's search form. I thought it was fascinating. The keywords it chose to search were generally meaningful words that occurred frequently on the site. I'm not sure if they were correlated with the Google search terms that hit my blog.
The corresponding SEO tip is to make sure that your site's search feature works, delivers good results for the keywords and delivers the results to which you want Google to pay attention.
I propose a new sport - Google Crawler hunting. Kind of like Snipe hunting, only you lay traps. Object is to see how long you can keep the Google bot there by generating new pages programmatically, and how many unique things you can get the bot to do.
What an interesting problem... so, if you were to build a searchbot, what would it type into those form fields it found?
It has to be very difficult, especially since you can't do too many submits. Could you somehow infer what to put in there based on searches in your own database already?
The corresponding SEO tip is to make sure that your site's search feature works, delivers good results for the keywords and delivers the results to which you want Google to pay attention.