Saab's mention of a BIOS timer sound like the answer, though mounting workload and a wife, possessive of her new toy, have limited my time on that problem somewhat. (No, writing rubbish on JB doesn't count. It's therapeutic.
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It was all to do with the Hibernate option causing the computer to be truly off, but since it only takes one pulse to turn a powered computer on, a very small signal from the Time-clock (using BIOS power) could do it. I'm surmising, but electronically, it could be the answer.