It is demonstrated that a closed delayed equation for the phase of the electric field can be used to describe accurately the transient switch on of a laser with external feedback when it can be described by field evolution equations. In contrast, it is shown that several more severe approximations to the dynamics, including an adiabatically evolving potential for one-dimensional relaxation dynamics (which had previously been used to accurately predict the laser linewidths for the steady-state solutions) fail to reliably describe the final state selection during transient switch on of the laser, the delay-induced oscillatory approach to the chosen state, and features of the amplitude and frequency spectra near multiples of the external cavity mode spacing which may be important for the stability and switching dynamics of the steady states that correspond to excitation of different external cavity resonances.