I took my dash harness out, unwrapped it, and found more than one circuit that needs replacing.
Chase down your short if you can. You'll at least need a test light, a volt ohmmeter will work also.
With the key in accessory position check both sides of the radio/ backup lamp fuse. If all is good there, you'll need to pull the harness and unwrap it to find the break and or short. Patch or replace the break/short.
I'm separating my b/u lamp power lead(white wire) and hooking it to the IGN 1 circuit with inline fuse at the bulkhead connector, this way I can listen to the radio in accessory position without the problem.