How can I standardize the query from exposed form input?

I apologize in advance if the title for this post is misleading, my intention is to use exposed form input from a form in a block display (not on the view page) to build a query on a page display for the same view. The page display has another exposed form block that filters on the same fields, plus others. When I submit input from the first form, the query looks like field_foo_target_id=123, which doesn't filter the view results. If I select the same input value on the exposed form on the page display, the query looks like field_foo_target_id[123]=123 and that works. I've noticed that when I step through HOOK_views_query_alter that the query argument for that field is a string, while it's of course an array in the second case. I thought maybe I needed to enable multiple values for each, which was only configured for the second field prior, but that hasn't solved the problem. I still think that this can be solved by fiddling with configuration, but I've tried several changes without success, so I thought I'd reach out to see if others may know off-hand why this discrepancy occurs.