The Wikipedia page on the Berlin Crisis of 1961 mentions the incident where an American soldier climbed into a T54 to see if it were a Soviet tank. It references the book Berlin 1961 by Frederick Kempe from 2011.
I've gotten access to Berlin 1961 on the Internet Archive. I couldn't "borrow" the book to read, but it turns out that you can search the book for specific words or phrases and access the pages found on search. Searching for "Pike" pulled up pages 470-471 (as well as several other pages.)
Wikipedia references pages 470 to 471 in Berlin 1961 as the source for the story about an American soldier entering a Soviet T54.
Here are those two pages:
sat atop their tanks, smoking, chatting, and eating dinner from mess kits.
West Berliners, held back behind rope barriers, bought pretzel sticks from street vendors, and presented flowers to GIs. The Western scene was all lit by enormous floodlights beamed from the communist side—an effort to intimidate using superior wattage. On the Eastern side, the apparently Russian tanks sat in darkness with their black-uniformed crews. "What a picture for the history books!" Schorr exclaimed.
Clay required confirmation for his masters in Washington that they were Soviet. It was not an academic point: for the U.S., the danger of a confrontation with Soviet tanks was that it could turn into a general war. East German tanks posed another sort of difficulty, because their deployment was prohibited in East Berlin under the four-power agreements.
Under orders to ascertain the tanks' origin, Pike and his driver Sam McCart climbed into an Army sedan and weaved through the barricades and down a side street well past the tanks, where they parked and then walked back. It was part of the surreal nature of the showdown that both sides continued to respect military freedom of movement at the border, so Pike could drive through without impediment.
Pike was surprised at the tanks' illogical two-three-two formation, which made it impossible for the rear tanks to fire upon the enemy. Beyond that, they also were making themselves easy targets. Pike walked up to the rear tank and saw nothing to help his investigation: "no Russians, no East Germans, no one." So he climbed onto the tank and down into the driver's compartment. There he confirmed it was Soviet by the Cyrillic script on the controls and the Red Army newspaper by the brake handle, which Pike could identify, given his smattering of Russian. "Hey, McCart, look at this," he said as he climbed out of the tank and showed him the newspaper that he had taken as evidence.
The tanks' crews, about fifty men in all, were sitting on the ground a short distance away, apparently getting briefed on their mission. Pike walked up close enough to hear they were speaking Russian. When one of the Soviet officers spotted him, Pike turned to McCart and said, "Let's get the hell out of here."
After driving back, they reported to Colonel Sabolyk, who was Pike's superior, that the tanks were Soviet. When Pike explained how he had found out and showed the newspaper, Sabolyk said in shock, "You did what?"
The disbelieving colonel put Pike on the phone to the emergency operations center, which connected him with Kennedy's special representative so he could hear for himself. "Whose tanks are they?" Clay asked.
"They are Soviet, sir," Pike said.
"How do you know?"
When Pike told him, Clay was silent on the other end of the line. Pike felt as though he could hear him thinking, "Oh, God, a lieutenant has started World War Three."
Pike had dared to undertake the mission partly because he felt young and invulnerable, but also because by then American soldiers thought little of Soviet discipline, morale, or military capability. Though GIs knew they were outnumbered, they also felt superior. When driving into West Berlin on the Helmstedt Autobahn from West Germany, Pike had seen Russian grunts hawking their belt buckles, caps, and even Soviet medals as souvenirs in exchange for Playboy magazines, chewing gum, ink pens, or especially cigarettes.
At less generous moments, GIs would flick burning cigarettes to the ground just to watch the Russians scramble to recover them for a few drags. Pike recalled later that their gear was of poor quality, their boots flimsy, their field jackets old; they looked to Pike like hand-me-downs from previous conscripts. He told friends that "their body odor would chase a buzzard off a shit wagon."
Pike had little more regard for their tanks, which maneuvered badly. The drivers were often from Asian minorities, Pike had noticed, because he reckoned they were the only ones able to fit into compartments that had been built too small. He and his men chuckled when the first tanks had rolled up that day and officers standing on the road struggled to position them using exaggerated hand movements and semaphores, apparently to overcome language and handling difficulties.
But nothing was very funny about Pike's realization that the Soviet…
Summary: US Army lieutentant Vern Pike crossed into the Soviet sector with his driver Sam McCart then proceeded to ascertain whether the tanks were Soviet tanks or East Germany tanks. The crews of the tanks were called away to a briefing, leaving the tanks unmanned. Pike entered one of the unmanned tanks and found (and took with him) a copy of a Red Army newspaper (in Russian.) The controls in the tank were marked in Cyrillic script as is used in Russian.
The book agrees with what was said in the video. The difficulty is that the passage in the book quotes an interview with Vern Pike by Frederick Kempe while the video is (apparently, I can't view the video here in Germany) of an interview with Vern Pike. Both sources are the same. All that tells you is that Vern Pike was consistent in his description of the events.
The book describes the entire evening of the incident. It started at just after 16:45. A group of American tanks had been present and left at 16:45. Shortly afterwards, a group of Soviet tanks became visible to Lieutenant Pike from the corner of Friedrichstrasse and Zimmerstrasse. He was sent to call back the American tanks. While he was gone, the Soviet tanks moved to a vacant lot on Unter den Linden (street) - that's several blocks north of Checkpoint Charlie. At 18:00, the Soviet tanks returned to Checkpoint Charlie and the faceoff began. It was sometime after 18:00 that Lieutenant Pike entered the Soviet tank.