Live Fields have access to the DOM, and can trigger events within it. In some cases, it can be helpful to users if the Table Field Indexer is open by default. A very simple script can trigger this behavior.
document.getElementsByClassName("tablefield-button").click(); return "Table Field Opened By Script";
Manipulating the DOM of the GlobalSearch Viewer is generally discouraged, but possible. Advanced users who go beyond very basic scripts like this one should use caution, and understand that elements your scripts rely on have and will change between version upgrades.