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Close dual quasars are expected to be common in the hierarchical universe. However comma very few confirmed dual quasars are known at <5 kpc at 1<z<3 comma in stark contrast to naive theoretical expectations. We propose STIS (G750L) slit spectroscopy to systematically discover close (<5 kpc) dual or strong gravitationally lensed quasars at redshifts 1<z<3. Our sample probes a new regime at higher redshifts comma higher luminosities comma and smaller merger separations than previous work. This poorly explored regime is crucial for understanding the effects of mergers in triggering quasar activity at cosmic noon. Our targets are selected using a new astrometric techniquedoublePoint when two close-by AGN vary stochastically comma their combined light centroid shifts comma which is detectable by Gaia. Follow-up dual-band HST imaging of Gaia-selected targets has recently uncovered multiple-cored morphology with small angular separations of virgul0.4d_comma-0.6d_comma comma subsequent to the most recent proposal deadline. The proposed STIS spectroscopy will unambiguously identify the targets as high-redshift close dual or lensed quasars and reject interlopers from chance superpositions with foreground stars-quasars. It will demonstrate the new astrometry technique and identify suitable targets for detailed JWST IFU follow ups. The program will provide a systematic pilot effort to fill the gap in our knowledge about the demographics of dual supermassive black holes on <5 kpc scales at cosmic noon.