The classical Cepheid eta Aql was not included in past Leavitt Law work because of a presumed complicating orbit due to a known B9.8V companion. To determine the orbit of eta Aql B, we analyze a significant number of radial velocity (RV) measurements from eight sources. With these we establish the RV variation due to Cepheid pulsation, using a model with 12 Fourier coefficients, while solving for velocity offsets required to bring the RV data sets into coincidence. RV residuals provide no evidence of orbital motion, suggesting either nearly face-on orientation or a very long period. Reanalysis of Hubble Space Telescope Fine Guidance Sensor astrometry now includes reference star parallax and proper motion priors from Gaia EDR3. As modeling confirmation, we reanalyze zeta Gem in parallel, deriving values for its parallax and proper motion consistent with Gaia EDR3, and consistent with the Benedict 2007 Leavitt Law. In an effort to further characterize eta Aql B, we hypothesize that eta Aql residuals larger than those of the associated reference stars or a parallax inconsistent with EDR3 and the Benedict 2007 Leavitt Law indicate unmodeled orbital motion. Using the astrometric noise or parallax mismatch with EDR3, we estimate possible periods and mass for eta Aql B. Ascribing photocenter motion to the photometric variation of the Cepheid, eta Aql A, yields a plausible separation that is consistent with a long period and explains the lack of RV variation. None of these approaches yields an unassailable characterization of the eta Aql A-B system.