We have measured excitation functions for the reaction $^{3}\mathrm{H}(\ensuremath{\alpha},^{6}\mathrm{Li})n$ at 0\ifmmode^\circ\else\textdegree\fi{} (lab) in an energy range covering the resonance corresponding to the 5/${2}^{\ensuremath{-}}$ state in $^{7}\mathrm{Li}$ at 7.46 MeV of excitation. A Ti-tritide target on a nickel backing was bombarded by an $\ensuremath{\alpha}$-particle beam, and the $^{6}\mathrm{Li}$ reaction products at 0\ifmmode^\circ\else\textdegree\fi{} were spatially separated from the beam in a magnetic field and were then detected in a thin solid-state detector. Data at 14 bombarding energies were obtained for the $^{6}\mathrm{Li}$ group emitted at ${\ensuremath{\theta}}_{\mathrm{c}.\mathrm{m}.}=0\ifmmode^\circ\else\textdegree\fi{}$, and data at 11 energies were obtained for the $^{6}\mathrm{Li}$ group emitted at ${\ensuremath{\theta}}_{\mathrm{c}.\mathrm{m}.}=180\ifmmode^\circ\else\textdegree\fi{}$. To normalize these reaction data we measured, simultaneously with the reaction, the yield of the elastically recoiling tritons at \ifmmode\pm\else\textpm\fi{}15\ifmmode^\circ\else\textdegree\fi{} and \ifmmode\pm\else\textpm\fi{}30\ifmmode^\circ\else\textdegree\fi{} (lab). We obtained absolute differential cross sections from the normalized reaction data by measuring excitation functions for $^{3}\mathrm{H}(\ensuremath{\alpha},t)^{4}\mathrm{He}$ at 15\ifmmode^\circ\else\textdegree\fi{} and 30\ifmmode^\circ\else\textdegree\fi{} (lab) using a gas target. The average error in the reaction data is 2.7%; the errors in the 15\ifmmode^\circ\else\textdegree\fi{} elastic data are less than 1%; the majority of the errors in the 30\ifmmode^\circ\else\textdegree\fi{} elastic data are less than 2%; and the \ensuremath{\alpha}-particle beam energy at the reaction region of the targets was determined to an accuracy of 6 keV. Our reaction data are compared with other data, data evaluations, and a recent three-channel multilevel $R$-matrix analysis of a large body of mass-7 data.NUCLEAR REACTIONS $^{3}\mathrm{H}(\ensuremath{\alpha},^{6}\mathrm{Li})n$, $^{3}\mathrm{H}(\ensuremath{\alpha},t)^{4}\mathrm{He}$, $E=11.3\ensuremath{-}12.0$ MeV; measured reaction $\ensuremath{\sigma}(E;0\ifmmode^\circ\else\textdegree\fi{})$, elastic $\ensuremath{\sigma}(E;15\ifmmode^\circ\else\textdegree\fi{}, 30\ifmmode^\circ\else\textdegree\fi{})$. Comparisons with other data, with data evaluations, and with three-channel, multilevel, $R$-matrix analysis.