Picture one person and one loop. A patrolman is the man who covers the same ground again and again — the same streets, the same stretch of road — so that he is already nearby when something goes wrong. The two meanings are the same loop with two different jobs waiting at the end of it: in American English he is the police officer on the beat, and in British English he is the man a drivers' club sends out to a car that has stopped.
From the word’s history
Wiktionary gives the word simply as patrol plus -man: the man who patrols. The -man ending is also why many police forces now prefer police officer or patrol officer.
Wiktionary 直接記 patrolman 是 patrol 加 -man，也就是「負責巡邏的那個人」。-man 這個字尾只指男性，這也是為什麼現在很多警察單位改用 police officer 或 patrol officer。
Wiktionary (kaikki extract, source_ref kaikki:3f6f69a190036ae4:1263004690): 'From patrol + -man.'
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