Details of the analysis of the $\ensuremath{\eta}{\ensuremath{\pi}}^{\ensuremath{-}}$ system studied in the reaction ${\ensuremath{\pi}}^{\ensuremath{-}}\stackrel{\ensuremath{\rightarrow}}{p}\ensuremath{\eta}{\ensuremath{\pi}}^{\ensuremath{-}}p$ at $18\mathrm{GeV}/c$ are given. Separate analyses for the 2\ensuremath{\gamma} and ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}$ decay modes of the \ensuremath{\eta} are presented. An amplitude analysis of the data indicates the presence of interference between the ${a}_{2}^{\ensuremath{-}}(1320)$ and a ${J}^{\mathrm{PC}}{=1}^{\ensuremath{-}+}$ wave between 1.2 and $1.6 \mathrm{GeV}{/c}^{2}.$ The phase difference between these waves shows a phase motion not attributable solely to the ${a}_{2}^{\ensuremath{-}}(1320).$ The data can be fitted by interference between the ${a}_{2}^{\ensuremath{-}}(1320)$ and an exotic ${1}^{\ensuremath{-}+}$ resonance with $M=(1370\ifmmode\pm\else\textpm\fi{}{16}_{\ensuremath{-}30}^{+50})\mathrm{MeV}{/c}^{2}$ and $\ensuremath{\Gamma}=(385\ifmmode\pm\else\textpm\fi{}{40}_{\ensuremath{-}105}^{+65})\mathrm{MeV}{/c}^{2}.$ Our results are compared with those of other experiments.