1979 Seville radio/clock question

We purchased a 1979 Seville through eBay a year and a half ago (dark blue exterior, lipstick red leather inside...she's sweet!) and have one small
problem with the car. The clock on the radio stays on even when the ignition is off. If we don't drive the car for a few days, the clock kills the battery. We have it on a trickle charger, but I'd rather just eliminate the problem if it's an easy fix. The radio still works and I'd like to keep it operative. The 8-track doesn't work, however. When I try to play a tape, the fuse for the radio blows. Perhaps this situation is related to the clock problem..
Any help?
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