BANGKOK—Thai accident investigators have begun a painstaking examination of a pleasure boat that sank in July, killing 47 Chinese tourists, with the goal of winning back the confidence of one of the single biggest contributors to Thailand’s economy.

Visitors from China make up nearly a third of the 35 million people who visit Thailand each year. Their spending has helped prop up an economy that has lagged behind its neighbors since a military junta seized power in 2014.