My 2 cents on this topic
whose is modifying branches because the prepositional phrase "on the branches" is modifying the verb "seen" and not monkeys. Hence "whose" cannot jump over the prepositional phrase and modify monkeys
If the sentence were something like the below
The monkeys of the savannah, whose ....blah blah - "whose" in this sentence modifying monkeys because the prepositional phrase "of the savannah" is modifying monkeys. Hence "whose"
...
whose is modifying branches because the prepositional phrase "on the branches" is modifying the verb "seen" and not monkeys. Hence "whose" cannot jump over the prepositional phrase and modify monkeys
If the sentence were something like the below
The monkeys of the savannah, whose ....blah blah - "whose" in this sentence modifying monkeys because the prepositional phrase "of the savannah" is modifying monkeys. Hence "whose"
...
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