Final answer:
The hyphen should be placed between 'half' and 'time' to form the compound adjective 'half-time' as it comes before the noun 'clock', resulting in: Eager for the game to start again, he watched the halftime clock.
Step-by-step explanation:
The hyphen in the phrase 'Eager for the game to start again, he watched the halftime clock' should be placed between the words 'half' and 'time' to form the compound adjective 'half-time'. Compound adjectives are often hyphenated when they come before a noun they modify, in this case, the word 'clock'. Thus, the corrected phrase should read, 'Eager for the game to start again, he watched the half-time clock.'