My eyes widen, and I slowly turn toward the elderly gentleman standing at my side.
In this sentence, before "standing", "who" is skipped why?
My eyes widen, and I slowly turn toward the elderly gentleman standing at my side.
In this sentence, before "standing", "who" is skipped why?
[1] My eyes widen, and I slowly turn toward the elderly gentleman [standing at my side].
[2] My eyes widen, and I slowly turn toward the elderly gentleman [who stands at my side].
The simple answer to your question is that although both examples are semantically similar, they have quite different grammatical structures: in [2] the nominal ("elderly gentleman") is modified by a relative clause while in [1] by a gerund-participial (-ing) clause.
The construction in [1] may be regarded as more succinct than [2] and thus perhaps generally more favoured.
There is no special 'rule' here, and although terms like 'reduced relative clause' and Whiz-deletion' are heard, and indeed may be mnemonically useful for some, they are actually misnomers. What we have here is simply post-head modification in NP structure by two different types of clause, a gerund-participial clause and a relative clause, not by a relative clause and some kind of 'hybrid' relative.
Edit: Note that the term 'reduced relative clause' comes from transformational generative grammar, which assumes deep structures and surface structures in language. Frameworks that assume no underlying form label non-finite so-called ‘reduced’ relative clauses as participial clauses.
You are in error. If you had only skipped the relative pronoun,
you would have produced the ungrammatical clause
In fact, in producing this sentence, you skipped a relative pronoun and an auxiliary verb is.
That is the effect of the syntactic rule mentioned above in comments, called Whiz-Deletion in the professional literature. It relates relative clauses with initial auxiliary be in their verb phrase (like relative clauses that have passives, progressives, predicate adjectives, or predicate nouns) to bare verb phrases modifying the antecedents of the relative clauses.
This doesn't mean one changes into another; that's silly -- language doesn't work that way (though writing occasionally might). It merely means the constructions are related grammatically, and share the same contexts and meanings, so if you understand one you understand the other; all you have to do is recognize the constructions and follow the rules.
In this case, the rule says that various unmarked verbal predicates can follow a noun, provided there is a grammatical relative clause with the same predicate, but following be and a relative pronoun subject.
The example sentence satisfies those conditions. And you followed the rule, even though you didn't realize you'd left out the auxiliary be, which is an illustration of why examples are more useful. Descriptions can leave stuff out or focus on the wrong things.
(By the way, imprecations to ignore other peoples' terminology are par for the course. Some people take this stuff too seriously. :-)