You could go all out with a logic circuit a two input AND gate. You sense two lines so you have to have this input AND that input to power up your radio. You could make it more complicated and I would be happy to draw that up for youJust had another thought...
I could wire the ignition switch to toggle the relay off if the radio is on already. This would prevent brain farts if I shut the truck off momentarily at a guard shack and then start it back up while the radio is on.