The development of covalent diazonium functionalization of carbon nanotubes brings unique opportunities in terms of original quantum sources of light. In particular, it should be possible to create a linear ensemble of closely packed single-photon sources along the carbon nanotube backbone. The physical proximity of several dopants would make it possible to couple them simultaneous to a resonant cavity mode and to induce original dynamics and light emission properties. Here, we investigate experimentally the case of a series of four quantum emitters attached to the same carbon nanotube coupled to a high finesse fiber cavity. We explore their properties through PLE, polarization and super-localization measurements and their light emission properties using time-correlation techniques and photo-luminescence decay measurements. We show that two pairs show qualitatively different behaviors in terms of spectral diffusion and luminescence saturation, which we interpret using two models of electronically coupled or uncoupled two-level systems.