A novel experimental approach to search for double electron capture (EC/EC) is discussed in this article. R&D for a new generation EC/EC spectrometer based on silicon pixel detectors (SPDs) has been conducted since 2009 for an upgrade of the TGV experiment. SPDs built on Timepix technology with a spectroscopic readout from each individual pixel are an effective tool to detect the 2vEC/EC signature of the two low energy X-rays hitting two separate pixels. The ability of SPDs to indentify alpha/beta/gamma particles and localize them precisely leads to effective background discrimination and thus considerable improvement of the signal-to-background ratio (S/B). A multi-SPD system, called a Silicon Pixel Telescope (SPT), is planned based on the experimental approach of the TGV calorimeter which measures thin foils of enriched EC/EC-isotope sandwiched between HPGe detectors working in coincidence mode. The sources of SPD internal background have been identified by measuring SPD radiopurity with a low-background HPGe detector as well as by long-term SPD background runs in the Modane underground laboratory (LSM, France), and results of these studies are presented.