OK then, I have found him on the China medal roll, and interestingly he's not listed in the company of any particular ship.
Gunner H.H Pettit, RMA6109 (so definitely the same chap) is shown as one of the 197 men garrisoning the North-West Fort at Taku. All no-clasp medals. Qualifying period for the garrison was 30th Jun to 31st Dec 1900