Very interesting question, though be careful of readings that might be too deep on this one! This section comes in Chapter 3 as you specify, when Finny has pretty much dragged Gene off to the beach for the day and they are walking on the beach along the Boardwalk. Both boys, seemingly simultaneously, remark that the other is drawing the attention of the people they pass:
I noticed that people were looking fixedly at him, so I took a look at myself to see why. His skin radiated a reddish copper glow of tan, his brown hair had been a little bleached by the sun, and I noticed that the tan made his eyes shine with a cool blue-green fire.
"Everybody's staring at you," he suddenly said to me. "It's because of that movie-star tan you picked up this afternoon... showing off again."
Notice that nothing more is said about this - either by Gene commenting internally on what he thinks or by Finny. It is as if both boys are embarrassed to continue the discussion. Some critics argue that this dialogue reflects an unspoken homoerotic tension between Gene and Finny that because of their youth and innocence they are not aware of. If this sounds particularly far-fetched, remember that the entire book is about boys interacting with boys, and the intensity of the relationship of Gene and Finny does suggest there might be more to it than a simple friendship. The above example does suggest that there is a deeply physical element to their relationship which intensifies the strength of their bond together.