Benamin or Benjamin Beeson? He doesn't appear to be listed in the Light Brigade casualties [died & wounded] on Kevin Asplin's site "The Asplin Military Resources" athometown.aol.co.uk/kevinasplin/home.html, but he does state there are inaccuracies in the original source material for those wounded as well as excluding those who died of disease.
If Lawrence Crider doesn't respond to your post here then try a new post rather than "tagging" your question on to an existing one.
Lawrence has actually written a book - In Search of the Light Brigade: A Biographical Dictionary of the Members of the Five Original Regiments of the Light Brigade from Jan 1,1854 to Mar 31,1856. Lawrence W Crider; [Oct 2004]; ISBN 898763127. It's the information included in it that he posts in his replies.
You could see if your nearest main or local library has or is willing to obtain a copy.