Referring back to my answer regarding the "PrincipalAxis" method, and the documentation:

For an $n$-variable problem, take a set of search directions $u_1,u_2,...,u_n$ and a point $x_0$. Take $x_i$ to be the point that minimizes $f$ along the direction $u_i$ from $x_{i-1}$ (i.e. do a line search from $x_{i-1}$), then replace $u_i$ with $u_{i+1}$.

Two distinct starting conditions in each variable are required for this method because these are used to define the magnitudes of the vectors $u_i$.

I think that the first parameter is the starting point, $x_0$, and, combined with the second parameter, thus define the magnitude of the search direction.

I suggest playing around with the magnitude of the second parameter, in that case, and perhaps using EvaluationMonitor[] to investigate the behaviour.

FindMinimum[x^2, {{x, 0.5}}, Method -> "PrincipalAxis", EvaluationMonitor :> Print["x = ", x]] 

Referring back to my answer regarding the "PrincipalAxis" method, and the documentation:

For an $n$-variable problem, take a set of search directions $u_1,u_2,...,u_n$ and a point $x_0$. Take $x_i$ to be the point that minimizes $f$ along the direction $u_i$ from $x_{i-1}$ (i.e. do a line search from $x_{i-1}$), then replace $u_i$ with $u_{i+1}$.

Two distinct starting conditions in each variable are required for this method because these are used to define the magnitudes of the vectors $u_i$.

I think that the first parameter is the starting point, $x_0$, and, combined with the second parameter, thus define the magnitude of the search direction.

I suggest playing around with the magnitude of the second parameter, in that case, and perhaps using EvaluationMonitor[] to investigate the behaviour.

FindMinimum[x^2, {{x, 0.5}}, Method -> "PrincipalAxis", EvaluationMonitor :> Print["x = ", x]]