'rarely-watched' is a compound of 'rarely' + 'watched'. 'rarely' derives from the adjective 'rare' (from Old French 'rar(e)', ultimately from Latin 'rarus' meaning 'sparse, uncommon') with the adverbial suffix '-ly'. 'watch' comes from Old English 'wæccan' (to be awake) and developed into the verb 'watch' meaning 'to observe'; 'watched' is the regular past/past-participle form.

'rare' came into Middle English from Old French 'rar(e)', itself from Latin 'rarus'. Middle English formed the adverb 'rarely' by adding '-ly'. Separately, Old English 'wæccan' led to Middle English forms like 'wacchen' and later modern English 'watch'; the past tense/past participle 'watched' is a regular development in modern English verb morphology. The compound 'rarely-watched' is a descriptive formation combining the adverb + past participle.

Originally, elements kept their original senses: 'rarely' meant 'sparsely/infrequently' and 'watch' (from 'wæccan') shifted from 'be awake' to 'observe'. Over time the compound came to specifically describe something that receives little viewing or attention ('seldom seen').