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 model...