Don't forget that there is power to the radio even when the switch is off. Both through the main radio harness and through the accessory overlay harness that exists on the SEEG. I've seen a radio have internal issues that would keep it in various ways more live than it should be even when the ignition switch was off.
That would not account for other accessories staying on though (if that's what you were describing -- I wasn't 100% sure). If that's what's going on you've got the range of potential problems from switch issues to wire chafes and contact. Unless something is obvious and if it can't be directly diagnosed my troubleshooting mantra is always: easiest and/or cheapest thing to try first.
That being so with what you're describing I'd pull connectors and look for water intrusion (or signs thereof), corrosion, etc. And when I say connectors I mean connectors everywhere. ECM, ignition switch, etc. While doing all that I'd spray electrical contact cleaner in the handlebar switches, ignition switch, anything else, blow it all out, rattle/feel test the switches, have an ohm meter handy. All the basic maintenance stuff. Be very methodical about it. Do a thing, one thing, check to see if can reproduce problem, then move on.
Fortunately none of that really costs anything. It can take some time. But eventually you'll track it down.