For “patrol”, the English to Latin Google translater suggests:
English meaning: noun: “a person or group of people sent to keep watch over an area, especially a detachment of guards or police”
English meaning: verb: “keep watch over (an area) by regularly walking or traveling around or through it.”
Latin nouns:
circuitio, circumitio: this describes the moving about but not the guarding
vigil, vigilia: this describes the guarding but not the moving about
excubiae: “out-bed-ness”: this centers on the idea of a man staying out of bed at night
Latin verb: excubias ago
Here is a description of Roman practice from Vegetius 3,8, cited in the L&S entry above:
ac de singulis centuriis quaterni equites et quaterni pedites excubitum noctibus faciunt. Et quia inpossibile uidebatur in speculis uigilantes singulos permanere, ideo in quattuor partes ad clepsydram sunt diuisae uigiliae, ut non amplius quam tribus horis nocturnis necesse sit uigilare. A tubicine omnes uigiliae committuntur et finitis horis a cornicine reuocantur. > idoneos tamen tribuni et probatissimos eligunt, qui circumeant uigilias et renuntient, si qua emerserit culpa, quos circumitores appellabant; nunc militiae factus est gradus et circitores uocantur.