Spacecraft observations of beat-like Langmuir waveforms on two orthogonal antennas in Earth's foreshock and the solar wind have been interpreted as beating associated with large-angle reflection of Langmuir waves from density inhomogeneities or nonlinear decay processes. However, the waveforms are often irregular, with uncorrelated waveform envelopes on orthogonal antennas. One interpretation is that irregular waveforms are a manifestation of the electromagnetic nature of Langmuir waves scattered to low wave numbers in the inhomogeneous solar wind. An alternative interpretation, investigated here, is that the shape of the waveform envelopes on orthogonal antennas becomes substantially different as Langmuir waves tunnel through evanescent regions, where the local plasma frequency in the inhomogeneous plasma exceeds the Langmuir wave frequency. We demonstrate that observations of uncorrelated waveform envelopes on orthogonal antennas are consistent with theoretical predictions for Langmuir wave tunneling in evanescent regions in the inhomogeneous solar wind. Incident Langmuir waves which are nearly aligned with the density gradient are also partially converted to transverse electromagnetic waves at the plasma frequency. The characteristic dual-antenna waveform signature of mode conversion is difficult to detect for typical solar wind parameters.