Using search_index_path I always got the absolute path back but for hosting on github a relative path is needed.
I wrote my own helper which uses link_to to get the relative path.
def link_to_search_index
absolute_link_to_index = '/' + extensions[:search].options[:index_path]
dom = Nokogiri.HTML(link_to '', absolute_link_to_index)
node = dom.at_xpath '//a'
node[:href]
end