Let's say on the river a scare card comes, an overcard completing a flush draw.

A player goes all-in for about 2/3 of the pot, there is one other player in position.

The all-in player holds his cards up with two hands in front of him, clearly visible to the players seated next to him.

In the absence of any other information, can you gain any information from a player showing cards in this way?

Isn't that illegal? I would ask to see his cards since he's showing others. There is the "show one show all" rule though I've only seen it invoked when shown to another player in the hand. If they aren't in the hand the guy probably just gets a warning.

Anyway...I think it is very polarizing. Every time I've seen this happen the guy has the effective nuts or a bluff.

SOSA does apply, but not during a live hand unless the Player has shown someone who is still in the hand.

I tend to think this Player has 'something' which may include the nuts. But I need to know what personality this Player is as well. Most 'people' wouldn't want to show a bluff since there could be a reaction from the other Players that see the cards that gives the 'Hero' additional information. Obviously the same could be said for holding the nuts as well ... and would these reactions be any different from said Players?

I would think that the tighter the Player image the more this will be the nuts. This type of Player probably wouldn't want to skew their image by showing a bluff and even less likely to show a premature bluff.

The looser Player may want to show off his bluff so that the Players around him can take in the moment 'together'. "See what vacillations I'm putting this guy through!!" However the same could be said for showing the nuts and embarrassing a Player for tanking so long in a no-win spot.

Interesting spots when they come up for sure .. GL

"... In the absence of any other information, can you gain any information from a player showing cards in this way? ..."

Yes.

Change seats to his left or right when able.

I think this will vary in meaning depending on whether he is friendly with the player beside him. I think they're more likely to show weak hands/bluffs to friends of theirs, and more likely to show strong hands to strangers.