Cary Cooper, a psychologist at Lancaster University in northern England, said Thatcher's souvenir provided an insight into the president's state of mind during the summit - he was bored.
"Here's a body, there's a head separate from the body," Cooper said. "Is he so unenamored with what's going on that he's having an out-of-body experience?
"The eye means I'm watching what's going on, I'm observing, but I'm not altogether there."
The documents confirm the immediate warmth between the two conservative leaders, who forged a strong anticommunist alliance during the 1980s. But they also reveal a lesser-known story - the lengths the U.S. administration went to to distance itself from Thatcher's then-unpopular government, which was facing a recession, rising unemployment, and inner-city riots.
Thatcher, prime minister from 1979 to 1990, was the first foreign leader Reagan invited to Washington for a state visit. The papers show she was briefed extensively ahead of the February 1981 trip on how to rebut criticism from the U.S. administration.
A briefing paper from senior adviser Alfred Sherman, marked "highly confidential," warns Thatcher of "ominous aspects" and "underwater snags" in the visit because of diverging interests.
On such issues as Latin America and the Caribbean, Americans "now expect Britain to see Caribbean problems in terms of America's strategic interest and not in terms of Britain's residual commitments in the area," Sherman wrote.
When the two leaders met in Washington, they struck up an immediate rapport. Thatcher considered the visit a triumph.
"The relationship gets warmer and warmer," Collins said. "After the February meeting, she's euphoric."
After the visit, Thatcher wrote to the British ambassador in Washington: "I have great confidence in the president. I believe he will do things he wants to do - and he won't give up."
Soon they were addressing their letters "Ron" and "Margaret"; the rest is history.
