I just received that timer module today and played around with it to see if it meets my needs. It's perfect! The default configuration isn't ideal, but the configuration options include what I needed to make it behave exactly as required to match the OEM head unit behavior.

When I actuate the trigger, the module energizes a relay for XX number of seconds or minutes (1 second to 60 minutes, selectable with a dial). So I can use the timer to shunt 12v from the constant power source to the ignition-switched power source for 30 minutes. A couple of diodes will ensure that I only power the entertainment system and nothing else. Technically the timer module can handle an 8 amp load, but I'll only be using it to energize a relay. I'm a big believer in using relays to actuate stuff.