Mad wiring??
The radio is switched and has power through the fuse only when the ignition switch is in the run or Acc position. If the dash harness has been previously hacked, you might have other issues within the harness. On my custom gauge installation for my 66 dash I am going to either piggy back off the fuse terminal or use the actual radio plug for my switched power to the gauges since the manufacturer wants switched power to the gauges running through a fuse.