Striker Benyon, also 19, has signed a two-year deal at Plainmoor after joining from Championship new boys Bristol City, where he was a prolific scorer for the reserve team.
Hinshelwood signed professional forms with the Seagulls at the start of last season having progressed through the youth ranks at the Withdean.
Benyon had loan spells at Crawley and St Albans last season and knows the ins and outs of Conference football.
Buckle told the Herald Express: "I am delighted to get both of them in. It's been hard work but very worthwhile because Paul and Elliott are players I really wanted.
"Paul is a bright 19-year-old who comes from a footballing family. I believe he deserves a chance. Elliott has a fantastic strike record and he did well out on loan last season."
Source: http://www.confguide.com/newsArticle.do?id=6669