URL of search results page does not always contain all keywords of the search query

When using quick "Search this forum..." or quick "Search this topic...", the URL of the search results page does not contain the parameter "keywords=". (also counts for using quick forum search that can be found in the header of a vanilla php3 board)

Further, when searching inside search results, the URL of the search results page only contains the parameter "keywords=" with the previous keyword(s), so without the latest added keyword(s).

However, when the search results consist of more than 1 page and you go to the next page, then the URL contains the parameter "keywords=" with ALL keyword(s).