[PatrickHenry]

My question: Under gravity, wouldn't the pendulum strings angle toward each other, exactly towards Newton's common point? But under accelleration, wouldn't the strings would be perfectly parallel?

They would gravitate toward each other under either circumstance (whether the elevator they were in was sitting on the ground or being lifted.) A passenger in the elevator wouldn't know which was the true situation.

[MonroeDNA]

"They would gravitate toward each other under either circumstance..."

Technically true, but under gravity they would always be closer than under accelleration.

Think of a strong gravity directly under them.