One of the primary open questions of astrobiology is whether there is extant or extinct life elsewhere the Solar System. Implicit in much of this work is that we are looking for microbial or, at best, unintelligent life, even though technological artifacts might be much easier to find. SETI work on searches for alien artifacts in the Solar System typically presumes that such artifacts would be of extrasolar origin, even though life is known to have existed in the Solar System, on Earth, for eons. But if a prior technological, perhaps spacefaring, species ever arose in the Solar System, it might have produced artifacts or other technosignatures that have survived to present day, meaning Solar System artifact SETI provides a potential path to resolving astrobiology's question. Here, I discuss the origins and possible locations for technosignatures of such a prior indigenous technological species, which might have arisen on ancient Earth or another body, such as a pre-greenhouse Venus or a wet Mars. In the case of Venus, the arrival of its global greenhouse and potential resurfacing might have erased all evidence of its existence on the Venusian surface. In the case of Earth, erosion and, ultimately, plate tectonics may have erased most such evidence if the species lived Gyr ago. Remaining indigenous technosignatures might be expected to be extremely old, limiting the places they might still be found to beneath the surfaces of Mars and the Moon, or in the outer Solar System.