The nub of this question is the problem of deciding who has the binoculars. (We'll assume there's only one pair.)
- 3 There is a soldier on the hill, whom he sees with binoculars.
is the only variant that properly disambiguates: 'with binoculars' is constrained to be the instrumental prepositional phrase attaching to 'sees'. The viewer ('he'), using binoculars, sees the soldier.
The other three variants do not disambiguate: either the soldier is carrying binoculars, or the viewer sees him using binoculars. Even with the commas, different stress patterns are possible in speech, which is more powerful at disambiguating. For instance:
- 4a There is a soldier on the hill, whom he sees, with binoculars.
If the independent clause is heavily stressed and the other comma-offset strings destressed, the default reading is that 'with binoculars' belongs with 'whom he sees'. BUT
- 4b There is a soldier on the hill, whom he sees, with binoculars.
If the independent clause and the final prepositional phrase are both heavily stressed and the relative clause destressed, the default reading is that 'with binoculars' belongs with '[the] soldier on the hill'. But the same punctuation is used. As others have said, the way to safely disambiguate to force the apparently unavailable sense in writing is to re-order:
- 5 There is a soldier with binoculars on the hill, whom he sees.
and gives the example 'The man saw the boy with the binoculars.' Here, 1, 2 & 4 are ambiguous,
– Edwin Ashworth Feb 17 '24 at 16:39