This paper reports on the development and testing of a novel, highly efficient technique for the injection of very rare species into electron beam ion traps (EBITs) for the production of highly charged ions (HCI). It relies on in-trap laser-induced desorption of atoms from a sample brought very close to the electron beam resulting in a very high capture efficiency in the EBIT. We have demonstrated a steady production of HCI of the stable isotope 165Ho from samples of only 1012 atoms (∼300 pg) in charge states up to 45+. HCI of these species can be subsequently extracted for use in other experiments or stored in the trapping volume of the EBIT for spectroscopic measurements. The high efficiency of this technique extends the range of rare isotope HCIs available for high-precision atomic mass and spectroscopic measurements. A first application of this technique is the production of HCI of the synthetic radioisotope 163Ho for a high-precision measurement of the QEC-value of the electron capture in 163Ho within the "Electron Capture in Holmium" experiment [L. Gastaldo et al., J. Low Temp. Phys. 176, 876-884 (2014); L. Gastaldo et al., Eur. Phys. J.: Spec. Top. 226, 1623-1694 (2017)] (ECHo collaboration) ultimately leading to a measurement of the electron neutrino mass with an uncertainty on the sub electronvolt level.