We determined the limb profile of the extremely Zeeman-sensitive emission line of Mg i at 12.32 μm (811.58 cm−1) during the May 1994 annular eclipse, using the 3.5-m ARC telescope at the Apache Point site on Sacramento Peak, New Mexico. Spectra were recorded at 0.1 cm−1 spectral resolution and 1 s time resolution using a cryogenic grating spectrometer. The time derivatives of the observed line energy and continuum intensity were used to infer high-resolution profiles of the solar limb. Data were obtained at second contact only, since clouds prevented observations at third contact. We find that the emission line energy peaks very close to the 12 μm continuum limb. This agrees with our result from the 1991 total eclipse over Mauna Kea, and also with non-LTE radiative transfer theory for this line, which predicts an upper-photospheric origin. However, in 1991, line emission remained observable as high as 2000 km above the continuum limb, whereas the 1994 data show observable emission to only 500 km. This difference greatly exceeds any applicable errors, or sensitivity differences in either data set, and must be attributed to spatial and/or temporal inhomogeneities in the solar limb emission of this line. We discuss possible causes of these inhomogeneities, and implications for observations at far-IR and submillimeter wavelengths.