present participle as a parenthesis

There were times, [listening to Arnold and narrowing his eyes in the same heat-struck gaze], when Jack felt turned about.

There are two ing-form participles here, "listening" and "narrowing", whose function is that of 'predicator'.

The bracketed element is an adjunct consisting of a coordination of two clauses functioning as a supplement, a loosely attached expression set off by intonation and punctuation, presenting supplementary non-integrated content.

It is possible for a relative clause to occur in postposed position where there is intervening material such as a supplement provided there is no confusion about the intended antecedent. Here, there is no doubt that "times" is the antecedent of "when".

Now, reading this question and focusing on its blurred image, I feel interested in its topic.

The clause between commas is an appositional and restrictive description of the subject’s state at the time or times defined by the start of the sentence.