After reading just about anything I could find on the draining issue, I think I found a very slick solution: I will just reroute the power supply for that circuit from the current "always hot" fuse, and instead supply the power from one of the accessory fuses which only become hot when the key is on. The I only need connect the clock to an always hot wire,and I will lose my trip meter settings which I do not care about, and voila....
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