  The interacting binary Eta Carinae remains one of the most enigmatic massive
stars in our Galaxy despite over four centuries of observations. In this work,
its light curve from the ultraviolet to the near-infrared is analysed using
spatially resolved HST observations and intense monitoring at the La Plata
Observatory, combined with previously published photometry. We have developed a
method to separate the central stellar object in the ground-based images using
HST photometry and applying it to the more numerous ground-based data, which
supports the hypothesis that the central source is brightening faster than the
almost-constant Homunculus. After detrending from long-term brightening, the
light curve shows periodic orbital modulation ($\Delta V$ $\sim$ 0.6 mag)
attributed to the wind-wind collision cavity as it sweeps around the primary
star and it shows variable projected area to our line-of-sight. Two
quasi-periodic components with time scales of 2-3 and 8-10 yr and low
amplitude, $\Delta V$ $<$ 0.2 mag, are superimposed on the brightening
light-curve, being the only stellar component of variability found, which
indicates minimal stellar instability. Moreover, the light curve analysis shows
no evidence of `shell ejections' at periastron. We propose that the long-term
brightening of the stellar core is due to the dissipation of a dusty clump in
front of the central star, which works like a natural coronagraph. Thus, the
central stars appear to be more stable than previously thought since the
dominant variability originates from a changing circumstellar medium. We
predict that the brightening phase, due mainly to dust dissipation, will be
completed around 2032 $\pm$ 4 yr, when the star will be brighter than in the
1600's by up to $\Delta V$ $\sim$ 1 mag.
