How do I configure Tooltips in a Resource File?

The tooltip's window is named "gtk-tooltips", GtkTooltips in itself is not a GtkWidget (though a GtkObject) and as such is not attempted to match any widget styles.

So, your resource file should look something like:

style "postie"
{
      bg[NORMAL] = {1.0, 1.0, 0.0}
}
widget "gtk-tooltips*" style "postie"