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Direct-collapse black holes (DCBHs) of mass ∼10⁴ − 10⁵ M_⊙that form in HI-cooling halos in the early Universe are promising progenitors of the ≳10⁹ M_⊙supermassive black holes that fuel observedz ≳ 7 quasars. Efficient accretion of the surrounding gas onto such DCBH seeds may render them sufficiently bright for detection with the JWST up toz ≈ 20. Additionally, the very steep and red spectral slope predicted across the ≈1 − 5 μm wavelength range of the JWST/NIRSpec instrument during their initial growth phase should make them photometrically identifiable up to very high redshifts. In this work, we present a search for such DCBH candidates across the 34 arcmin²in the first two spokes of the JWST cycle-1 PEARLS survey of the north ecliptic pole time-domain field covering eight NIRCam filters down to a maximum depth of ∼29 AB mag. We identify two objects with spectral energy distributions consistent with theoretical DCBH models. However, we also note that even with data in eight NIRCam filters, objects of this type remain degenerate with dusty galaxies and obscured active galactic nuclei over a wide range of redshifts. Follow-up spectroscopy would be required to pin down the nature of these objects. Based on our sample of DCBH candidates and assumptions on the typical duration of the DCBH steep-slope state, we set a conservative upper limit of ≲5 × 10⁻⁴comoving Mpc⁻³(cMpc⁻³) on the comoving density of host halos capable of hosting DCBHs with spectral energy distributions similar to the theoretical models atz ≈ 6 − 14.