Searching summary fields generally wouldn't make sense, anyway. Likewise for global fields.
As for button fields, you can have your button script go to the field if in find mode, and yes, you can search by them.
a lot of things can be searched... go into layout mode and from the View menu select show -> Quick find. If it has a magnifying glass, it can be searched. ( If the magnifying glass is orange, it will take more time. )
If you have a button on a field that you want to be searched, put something like this at the beginning of the script: if (get(windowmode0 = 1) ) go to field x).
Another solution is to use script triggers instead. The script triggers can be set to run in browse mode but not in find mode.
You can't search summary fields because they don't contain a value that can be ascertained until you have a found set. And, exactly the same value may be valid for any number of found sets.
As far as I know, the only type of field that cannot be searched is a container.
In addition: If the field has tab order, you can go into the field without clicking.
Thanks to all of you for responding. Sorry for my delayed reply. All helpful stuff.
My issue was being able to quickly find a subset out of about 1.5 million records in a table. That was my motivation for trying to search summary fields and count fields in which I had stored values that flagged the records I need to look at most often. Neither worked. A calculation field used to flag the records can be searched but it takes forever because calculation fields are not indexed. I finally solved the problem with what should have been obvious: a self-join. I can search the related field in a self-join and the search takes about two seconds.