One morning I shot an elephant in my pajamas. How he got into my pajamas I'll never know.
That's a joke. It relies on an ambiguity in English grammar. On the one hand, the phrase "in my pajamas" is in a good place to modify the verb "shot". On the other, it's in a good place to modify the noun "elephant". Grammar alone can't tell us which word this phrase modifies.
My dad spotted the whale looking through his binoculars.
This sentence has the same structure and the same ambiguity as the first sentence of the joke. The phrase "looking through his binoculars" is in the right position to modify either the verb "spotted" or the noun "whale".
It is not in the right position to modify "dad" as either a restrictive or nonrestrictive phrase.
The model sentence is correctly punctuated.
My dad, looking through his binoculars, spotted a whale.
When the participial phrase does modify "my dad" directly, then we can use parenthetical commas to mark that it is nonrestrictive.