Head unit ignition switch wire has constant power

It sounds like your wiring harness (the car side) is miswired, i.e. your switched power is actually constant power. You need to fix this so that the switched power terminal actually uses switched power.

Easiest thing to check is to remove the head unit (and as much of the surrounding plastics as practical) and peer into the wiring on the car side. From the factory you should have wires going into OEM terminals. A well-done head unit install uses an adapter harness that looks like this:

If you have wires changing colors, random electrical tape, homemade-looking connections that's your cue that someone was in there and hacked the wiring.

Next, look online for a wiring diagram for your vehicle for the head unit. These are generally widely available. Verify that the wires you are looking at in your vehicle match the colors that the wiring diagram says they are supposed to be.

If you go far enough into the harness you SHOULD find the proper OEM wire colors and proper functions.

If you can't figure this out, a hacky way out of the situation is to find some other switched power source. Most things on the car use switched power so this shouldn't be too difficult. Problems with this approach:

• Your radio will be on some random fuse.
• You could overload that fuse.
• You could have electrical interference from whatever else is on the circuit you'd be using.
• The fuse may be rated too high and your radio may burn out in a short.