We examine the long-term spectroscopic and photometric variability of EX Lupi and TW Hya, studying the presence of stable accretion and the role it plays in the observed variability. Analysing the velocity modulations of the emission lines with STAR-MELT, we obtain information on the structure of the accretion columns and the disk-star connection. The emission line radial velocities reveal that TW Hya, like EX Lupi, has a remarkably stable or slow-varying accretion column footprint, locked to the star for several years. The line-emitting regions are non-polar for both EX Lupi and TW Hya, and species with different energies differ in position. In contrast, the continuum emission as observed in the photometry is very variable and can be modelled by hot spot(s) that change over time in phase, shape, temperature, size, and location with respect to the emission line region. The continuum emission region may not be limited to the stellar surface, especially during episodes of high accretion. The broad line emission observed in EX Lupi during episodes of increased accretion reveals a further structure, which can be fitted by non-axisymmetric disk in Keplerian rotation inwards of the corotation radius. Since the radial velocity modulation due to accretion footprints is so stable, we used it to search for further velocity modulations. While no residual modulation (other than caused by stellar rotation) is found in these objects, a similar analysis could help to identify young planets/companions. Therefore, determining whether stable accretion footprints are common among young stars is a key to detect young planets.