A single crystal of a rare-earth random-site alloy, Ho_0.5Er_0.5, has been studied with X-ray diffraction. We have used the technique of resonance-enhanced scattering at the Ho and Er L_III absorption edges to study element-specific effects in the temperature dependence of the magnetic structure below the Neel temperature. In the highest-temperature phase, a c-axis modulated structure in which the Ho and Er moments take different tilt angles from the basal plane, measurements at the two edges show identical satellite positions. The lowest temperature phase, a conical spiral which locks to a structure with wavevector ⁹/₄₀c^* below 20 K, is accompanied by a basal-plane lattice modulation that is related to the magnetic structure. The modulation changes the symmetry of the crystal lattice; as a consequence we suggest that the magnetic structure locks to one with equidistant spin-slip discommensurations. In addition, we find an unusual energy and polarization dependence in the satellite intensity in this phase that is not seen at higher temperatures. We present arguments to demonstrate that the unusual behaviour is not accounted for by multiple-scattering events.