We present a comprehensive multiwavelength temporal and spectral analysis of the fast rise exponential decay GRB 070419A. The early-time emission in the gamma-ray and X-ray bands can be explained by a central engine active for at least 250 s, while at late times the X-ray light curve displays a simple power-law decay. In contrast, the observed behaviour in the optical band is complex (from 10(2) up to 10(6) s). We investigate the light-curve behaviour in the context of the standard forward/reverse shock model; associating the peak in the optical light curve at approx 450 s with the fireball deceleration time results in a Lorenz factor Gamma approximate to 350 at this time. In contrast, the shallow optical decay between 450 and 1500 s remains problematic, requiring a reverse shock component whose typical frequency is above the optical band at the optical peak time for it to be explained within the standard model. This predicts an increasing flux density for the forward shock component until t 4 x 10(6) s, inconsistent with the observed decay of the optical emission from t 10(4) s. A highly magnetized fireball is also ruled out due to unrealistic microphysic parameters and predicted light-curve behaviour that is not observed. We conclude that a long-lived central engine with a finely tuned energy injection rate and a sudden cessation of the injection is required to create the observed light curves, consistent with the same conditions that are invoked to explain the plateau phase of canonical X-ray light curves of gamma-ray bursts.