He could feel it through a shared chakra link. Since they are related and Minato sealed the Nine - Tails in Naruto, there might be a latent connection that gets activated in the fanfiction, allowing him to sense Naruto's pain on a physical and emotional level.
In some fanfictions, Minato is made to relive Naruto's life events in a dream - like state. As he witnesses Naruto's experiences second - hand, he can't help but feel the pain that Naruto has gone through. This includes not only the physical harm but also the emotional distress, like Naruto's longing for acceptance and his heartache over lost friends.
The plot could involve Minato being brought back to life or having a vision where he steps into Naruto's shoes. He might feel Naruto's pain from constantly being underestimated because of his status as a Jinchuriki. This could lead to Minato trying to find ways to comfort Naruto from afar, or even influencing the events around Naruto in a supernatural way.
There are many out there. A really good one might focus on the emotional reactions of Team Minato. For example, Minato might be proud of Naruto's strength and how he overcomes Pain. Kakashi could be in awe at Naruto's new techniques. Their reactions can enhance the overall viewing experience in the fanfiction.
One of the main similarities is their self - sacrifice. Minato sacrificed himself to save the village and his son. Naruto has also shown that he is willing to put himself in harm's way for the greater good. He's always the first to jump into a dangerous situation if it means protecting those he loves. Another aspect is their leadership qualities. Minato was a great leader as Hokage, and Naruto has developed into a great leader as well, inspiring those around him.
Minato's presence can have a huge impact. He can act as a mentor, teaching Naruto things he never knew about his family and heritage. His wisdom and skills can inspire Naruto to reach new heights in his training and ninja development.
Maybe it's some kind of special jutsu or a curse that backfires in a way that numbs his pain receptors. For example, a powerful sealing technique might have been placed on him accidentally or on purpose that has this side - effect.
You can try looking on popular fanfiction websites like FanFiction.net or Archive of Our Own (AO3). They usually have a wide range of Naruto - related fanfictions, and you should be able to find some with the 'Team Minato Watches Naruto vs Pain' concept.
His fighting style could become more aggressive. Without the fear of pain, he might be willing to use more extreme techniques that would otherwise be too dangerous because of the pain they cause to the user. He could push his body to the limit more often.
Emotionally, Naruto would become more confident and stable. Having his father back would fill a void in his heart. This new - found emotional strength could translate into better chakra control and more powerful jutsu. Minato could also guide Naruto in handling the power of the Nine - Tails more effectively.
It would be very close. Naruto has always longed to know his father, so when he travels back in time to meet Minato, they would quickly bond. They'd probably start training together right away.
Naruto, like Minato, might show prodigious skills in areas such as combat and strategic thinking. Minato was known for his speed and his ability to quickly analyze situations. Naruto could be depicted as having similar traits, perhaps with his own unique spin. For example, Naruto might have an uncanny ability to learn new jutsu quickly, just as Minato was able to master complex techniques at a young age.