Motivated by the potential use of electromagnetically induced transparency (EIT) to measure atomic parity nonconservation (PNC), we have studied EIT and associated optical rotation for a three-level system in thallium vapor. EIT allows sub-Doppler resolution of the ${6P}_{1/2}\ensuremath{\rightarrow}{6P}_{3/2}$ mixed magnetic dipole, electric quadrupole transition at $1.28\ensuremath{\mu}\mathrm{m}$ when $0.535\ensuremath{-}\ensuremath{\mu}\mathrm{m}$ radiation acts on the ${6P}_{3/2}\ensuremath{\rightarrow}{7S}_{1/2}$ transition. Our measurements include rotation due to electromagnetically induced birefringence and Faraday rotation perturbed by EIT. We also identify a new method for determining the amplitude ratio $E2/M1$ for the $1.28\ensuremath{-}\ensuremath{\mu}\mathrm{m}$ transition. The possible advantages of an EIT technique for measuring atomic PNC are discussed in the context of our results.