"I kind of saw myself in him," Bomer told PEOPLE on the red carpet for the PaleyFest tribute to his series American Horror Story.
Of course, their physical resemblance is uncanny – something even Bomer noticed long ago.
"Even as a young kid – before obviously I knew anything about him, or even myself – I saw him on screen and I thought, 'Oh wow he actually looks a lot like my brother,' " said Bomer.
But it was Clift's story away from the big screen that really captivated Bomer.
"He was one of those really early screen icons for me to start with," Bomer, 38, said. "Then once I learned the circumstances of his life, I realized how he was someone who did not want to be relegated to the times he lived in and was so progressive in so many ways."
One of the earliest and best-known proponents of the immersive, naturalistic "Method" school of acting alongside Marlon Brando and James Dean, Clift quickly went from Broadway sensation to Hollywood leading man, headlining now-classic films like A Place In the Sun, From Here to Eternity and Raintree County.
But Clift’s movie star good looks were marred by a 1956 car accident that, despite cutting-edge plastic surgery at the time, altered facial features and left him with chronic medical conditions as well as drug and alcohol dependencies.
Emotionally, Clift also struggled with his sexual orientation during the repressive era, compounded by his place in the spotlight and an intense desire to keep his personal life private.
Even as he wrestled with personal demons and his emotional conflicts, he added more compelling performances – including Judgment at Nuremberg and The Misfits, which marked the last screen appearances of both Clift and his friend and costar Marilyn Monroe – before his death of a heart attack at age 45 in 1966.
"He had to deal with so many things that we don't have to deal with as much these days," explained Bomer. "So I thought it was an important story for people to remember."
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The White Collar actor said he wants another generation to know just how much of a pioneer Clift was in his own era.
"It's crazy how many people I talk to, especially under 30, who don't know who Montgomery Clift is. What?" he revealed. "I feel like someone is responsible for letting people know how important he was – culturally, socially, but most importantly as an artist."
Bomer reveals that the long-gestating screenplay is still underway, with the project having found a home at HBO last year.
"It's a hard story to tell, which is why we haven't had his biopic yet," he said. "But it's going great. It's in development. We're just not going to make that movie unless it's the right movie and it's told right and done right."