Ziegler–Nichols method, use time value of 63% of process variable or steady-state level line?
The Ziegler-Nichols method is a heuristic, it works well for a lot of systems but it is no guarantee of any "optimality" (as no system is really linear, or time invariant or just of 1st or 2nd order). That said, both those methods seem ok (as a mean to get an approximation of the system) and they will probably yield close models, but, I would say the first one is easier for real system (as you will not get smooth data to find where the inflection happens).

They both derive from the step response of a first-order model

$$ y(t) = C(1-e^{-t/\tau})$$

The first one uses that "magic number" which is actually

$$ C \;0.63 \approx C(1-e^{-1}) = C(1-e^{-t_e/\tau}) \Rightarrow -1 = -t_e/\tau$$ 
$$ t_e =\tau.$$

The second one and its inflection point is a way to approximate that

$$ \dot{y}(t) = Ce^{-t/\tau}/\tau$$
$$ \dot{y}(0) = C/\tau$$

So, by knowing the gain \$C\$ and finding the line that starts at the point x-y (L,0) and is tangent to the curve at some point of the curve, you would be able to find \$\tau\$.