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Recent near-IR power-spectra and panchromatic Extragalactic Background Lightmeasurements provide upper limits on the near-IR surface brightness (SB>31mag/arcsec^2) that may come from Pop III stars and accretion disks aroundresulting stellar-mass black holes (BHs) in the epoch of First Light (z=7-17).Physical parameters for zero metallicity Pop III stars at z>7 can be estimatedfrom MESA stellar evolution models through helium-depletion, and for BHaccretion disks from quasar microlensing results and multicolor accretionmodels. Second-generation stars can form at higher multiplicity, so that BHaccretion disks may be fed by Roche-lobe overflow from lower-mass companions intheir AGB stage. The near-IR SB constraints can be used to calculate the numberof caustic transits behind lensing clusters that JWST and the 25~39 mground-based telescopes may detect for both Pop III stars and stellar mass BHaccretion disks. Because Pop III stars and stellar mass BH accretion disks havesizes of a few x 10^-11 arcsec at z>7, typical caustic magnifications can bemu=10^4~10^5, with rise times of hours and decline times of < 1 year forcluster transverse velocities of v<1000 km/s. Microlensing by intraclustermedium objects can modify transit magnifications, and lengthen visibilitytimes. Depending on BH masses, accretion-disk radii and feeding efficiencies,stellar-mass BH accretion-disk caustic transits could outnumber those from PopIII stars. To observe Pop III caustic transits directly may require monitoring3~30 lensing clusters to AB< 29 mag over a decade or more. Such a program mustbe started with JWST in Cycle 1, and -- depending on the role of microlensingin the Intra Cluster Light -- should be continued for decades with the GMT andTMT, where JWST and the ground-based telescopes each will play a unique andstrongly complementary role.

On the observability of individual Population III stars and their stellar-mass black hole accretion disks through cluster caustic transits