Final answer:
The clues suggest that the man is a plumber who uses a plumbing snake to unclog drains, and his labor get rewarded with payment after resolving a plumbing issue.
Step-by-step explanation:
The clues provided in the prompt suggest that the man in question is likely a plumber. The mention of encountering snakes likely refers to the use of a plumbing snake, a tool used to unclog drains, and the phrase "the man wrestles with the snake behind closed doors" seems to imply that he is working in a private area such as a bathroom. The fatigue and sweating could come from the physical labor involved in plumbing work, and the owner's reaction—relief and payment—supports the job being service related. The clues do not fit the other professions; detectives and lawyers deal with legal matters, exterminators handle pests, and handymen perform a variety of repair tasks but the specific mention of snakes and valuable goods is distinctive of a plumber resolving a plumbing issue.