What's the word for a sycophant who imitates the words of his idol?

Solution 1:

A parrot

a person who repeats or imitates the words or actions of another unintelligently; a person who mechanically repeats the words or acts of others, usually without full understanding (Collins)

You would be surprised how often you can find this word in the Hansard:

• In his intervention the Minister sounded like a parrot mouthing the words of Mr Peterken. However, perhaps Mr. Peterken is the parrot repeating the Minister's words. (House of Commons, 13 March 1990)
• There is no point in the Minister repeating like a parrot, " It's wrong: " It is not wrong. (House of Commons, 16 January 2002)