A measurement of the Stark-induced amplitudes \ensuremath{\alpha} and \ensuremath{\beta} for the 6
P1/2\ensuremath{\rightarrow}7
P1/2 transition in atomic thallium is reported. Absorption of cw laser light tuned to this transition at 293 nm was compared to absorption of 378-nm cw laser light tuned to the allowed 6
P1/2\ensuremath{\rightarrow}7
S1/2 transition. The absorption sample was an intense atomic beam in the presence of a strong electric field. The measured values are \ensuremath{\alpha}=2.01(4)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}5}$ ${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$/ (V/cm) and \ensuremath{\beta}=1.67(4)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}5}$${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$/ (V/cm), where ${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$ is the Bohr magneton. These results are in agreement with semiempirical theory, but disagree with previous measurements of these amplitudes in this laboratory. A critical analysis of the previous measurement is given to explain the discrepancy. The newly measured value of \ensuremath{\beta} makes it necessary to reinterpret previous measurements of parity nonconservation in the 6
P1/2\ensuremath{\rightarrow}7
P1/2 transition. In the course of the present experiment, Stark shifts of the 6
P1/2\ensuremath{\rightarrow}7
P1/2 and 6
P1/2\ensuremath{\rightarrow}7
S1/2 transitions were also measured: \ensuremath{\Delta}\ensuremath{\nu}(6
P1/2\ensuremath{\rightarrow}7
S1/2)=-112(6) kHz/(kV/cm
)2 and \ensuremath{\Delta}\ensuremath{\nu}(6
P1/2\ensuremath{\rightarrow}7
P1/2)=-618(31) kHz/(kV/cm
)2. These results are also in good agrement with semiempirical theory.