In a previous paper the authors proved the existence of various pairs\break (A(q),B(q)) of lacunary eta quotients with identically vanishing coefficients. Further experiments indicated that the results in this previous paper were just the "tip of the iceberg". We provide a comprehensive description of what experiment suggests and employ a variety of methods to prove experimentally-derived results. The work is a template and atlas for the subsequent study of lacunary eta quotients. A broad range of proof strategies are applied to confirm the vanishing structure. These comprise a representative sample of techniques that may be used to study the remaining observations and conjectures resulting from the work.

Dongxi Ye was supported by the Guangdong Basic and Applied Basic Research Foundation (Grant No. 2023A1515010298).