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.
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.'
Two branches
在街上巡的警員（美式）
這一支就是核心畫面本身：同一塊地方，一再走過。
noun · B2
A police officer whose job is to walk or drive around the same area again and again, to stop crime and to deal with whatever happens there. In American English it is also a rank: the officer out on the street, below the ones who investigate or supervise.
巡邏警員
在公路上跑的道路救援（英式）
同一條「在一區裡來回跑」的路線，只是他要趕去的不是案件，而是一台熄火的車。
noun · C1
In Britain, someone who works for a drivers' association and drives out to help members whose car has stopped working by the side of the road.
（英）道路救援人員