"He held his index finger up with an air of importance." The gesture of holding up his index finger with an air of importance could imply that he was about to make a significant point or share an important piece of information. However, the frown on his face could suggest that whatever he was about to say was not pleasing to him or perhaps even something that was difficult for him to share.
Maybe there was some skepticism or uncertainty in his tone and that was the reason behind his frown. It could also be that he was hesitant to share his thoughts, but felt obligated or compelled to do so. Whatever the reason, the juxtaposition of the confident gesture and the uneasy expression made the situation even more intriguing and left the observer curious about the outcome of the conversation.
In conclusion,
The gesture of holding up the index finger implies important information and a frown suggests unease, skepticism, or hesitation. The observer is left curious about the outcome of the conversation.