If the change in the rate of the pendulum is due to a change in the force of gravity, I don't see why a scale wouldn't measure the effect far more accurately.
If the change in the rate is due to a distortion of spacetime, I don't see why an atomic clock wouldn't measure the effect far more accurately.
"If the change in the rate is due to a distortion of spacetime, I don't see why an atomic clock wouldn't measure the effect far more accurately."
(I was in Munich to film the eclipse in 1999, but I certainly didn't have an atomic clock)
On the Behaviour of Atomic Clocks during the 1999 Solar Eclipse over Central Europe
Article
http://www.mpq.mpg.de/~haensch/eclipse/full.html
No evidence found of time distortion during eclipse
--abstract from article -
Previous reports on detected influences of solar eclipses on atomic clocks and the movement of pendulums have brought up speculations that some yet undetected gravitational shielding effect exists. We have compared the relative pace of three types of atomic clocks, based on the ground state hyperfine transitions of hydrogen, rubidium and cesium during the total solar eclipse on 11th of August 1999 over central Europe. In our experiment, no anomalous changes in the relative clock rates correlated with the eclipse were found, at a level much smaller than previously reported.