Botherway kicked a penalty just after halftime and Hamilton then appeared to have established a comfortable margin when prop Liam Van Der Heyden burst through to extend the lead to 29-15.
But two tries to Gose narrowed the gap to 29-27 and with time up on the clock, they mauled their way over in the corner for the narrow win.
Hamilton coach Cam Moorby said the loss was difficult to digest.
“Gose are a very good team with a strong forward pack and a very accurate first-five who kept us pinned in our half at critical moments,” he said.
“A lack in discipline on our behalf combined with the language barrier caused a breakdown in communication on some law interpretations and ultimately we didn’t adjust well enough, particularly around the ruck and maul area.
“We’ve taken a pretty hard lesson and will be better for it come Thursday.”
Of Thursday’s match, Moorby said: “All we can do is control our own build up. That’s one benefit of these short turnarounds. You get the opportunity to put disappointment behind you pretty quickly.
“The boys will be ready to go again.”
Tokai University Sagami were beaten 19-14 by Nagasaki Hokuyodai High and 28-25 by Gose on Tuesday.
Meanwhile in girls sevens play, Howick College beat Reitaku High School (Japan) 31-14 and Hong Kong China Junior Dragons 35-7, but lost 17-0 to Kanto Gakuin Mutsuura High (Japan) and Fukuoka Rugby Football Club 27-5.