Post-silicon validation is the time-consuming process of detecting and diagnosing defects in prototype silicon. It targets electrical and functional defects that escaped detection during pre-silicon verification. While the at-speed execution of test scenarios facilitates a higher test coverage than pre-silicon simulation, this comes at the cost of limited observability of signals in the integrated circuit. This limitation complicates the localisation of the cause underlying a defect. Trace buffers, designed to store a limited execution history, partially alleviate but do not entirely remedy the problem. Since trace buffers typically record only a small fraction of the system state over at most a few thousand cycles, their utility is contingent on the cautious selection of traced signals. This paper presents a technique for the automated selection of trace signals. While the aim of existing selection strategies is typically to enable the (early) detection of defects or to maximise the recoverable state information, our objective is to facilitate the subsequent automated localisation of faults using consistency-based diagnosis. To this end, we use integer linear programming and automated test pattern generation to identify a subset of state signals through which potential failures are likely to propagate. We demonstrate that our technique complements our previous work on SAT-based fault localisation using backbones. In that context, we evaluate the utility of our results on two OpenCores designs. We show that for this purpose, our technique generates a better selection of trace signals than a related approach recently presented by Yang and Touba.