What grammatical construction is the idiom "to look the part"

Question

Normally, "look“ is used with prepositions like "at, towards". However, there is this neat construction "to look a part / one's age etc.".

Is this just a shortened version of a comparison with like?

E.g.

Se looked (like someone at) his age

She looked (like an actor playing) the part

Or is it a grammatical construction where look can take a direct object?

Answer 1

1. I'm coming to the conclusion I don't look my age, and I don't act my age. (source)
2. In his cowboy hat and boots, he certainly looked the part. (source)

In both of these, look is a complex-intransitive¹ verb, with my age and the part functioning as predicative complements (PCs), not as objects (Os).

The criterion we can apply to both is exchanging the noun phrases (NPs) with adjective phrases (AdjPs) (I'm coming to the conclusion I don't look good_AdjP; he certainly looked handsome_AdjP) or bare role NPs, as they are both admissible as PCs, but not as Os.

Another criterion, which isn't sufficient, but is necessary, is that a PC can't be the subject of the corresponding passive clause (^{_{UNGRAMMATICAL}}my age is looked by me; ^{_{UNGRAMMATICAL}}the part was looked by him), which an O could be.

I'd regard both expressions as idiomatic in meaning, but I don't see why the above analysis wouldn't apply anyway.

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¹ a term used in The Cambridge Grammar of the English Language (2002) by Huddleston et al., whose analysis I've tried to follow in this answer