The Global Site Search plugin creates a form that breaks accessibility guidelines in two ways:
1. It uses a <table> for layout (which has been deprecated for years)
2. It doesn't have a <label> for the <input> field or a title attribute. Either of these would be fine.
Could you please look at addressing these issues in a future update? In the meantime, I've modified my own copy of the plugin to remove the table and add a title attribute.