You could build your own 555 timer circuit tho I understand the DEI 528T is based on a 555 so it may be easier to modify that (increase the timing capacitor size).
Otherwise there are various timer circuits available as kits, tho I choose to build my own with the exception of the DEI 528T. (Not that I have bought one yet, but I considered it cheap enough to warrant avoidance of DIY resources.)
I haven't investigated the logic you propose - I'll leave that to others ((ie, switching & control).
But re that, and the "interesting" link you provided, I've always had my radio/HU powered direct from the battery, tho recently I did involve my IGN circuit due to the high drain (~130mA) when off with both constant and switched supplies at +12V (due to newer USB etc inputs).
In that case I rigged an ignition (tho normally that would be be ACC) actuated relay which latched on using the HU's remote output, hence requiring IGN (else ACC) to enable the HU to be switched on but it then stayed on until I turned it off. (The relay connected my heavy fused battery constant to the HU's switched power input.)
I was going to add a switch to enable ON without IGN; or OFF when IGN turns off as well as my default ON with IGN but manual off.
If I were to add a timer function, I would have used a PICAXE 08M2 since it's almost as cheap as a 555 timer but fully programmable (no caps or resistors to change), but in part that was due to a similar function for my dash mounted 3-digit voltmeter. (That used an IGN actuated PCB relay to connect its +12V direct to battery +12V, but likewise that was later intended to have an
on anytime as well as a timed option - ie, stay on for 2 minutes after IGN off, or 2 minutes after a momentary
on anytime switch actuation.)
When I fitted electric windows to the same 49 year old vehicle I used a constant supply. Likewise that was to have an added lock (deactivate) switch and IGN-only option, possibly with timer (eg, can open or close up to say 2 minutes after IGN off) similar to above but also with and auto-open & auto-close (and safety) feature using current sensing, and a (default) delayed auto-close after IGN off.
Apols for the rant but I'm showing my preference for "always available" accessories like HUs, windows, wipers, some monitoring, camera recording etc, else that they be user selectable despite their OEM or default IGN/ACC powering.
And the PICAXE comes in due to its "one circuit fits all" - only the program varies (unless I use a universal program with automated sensing else some user configured component/switch that determines its application) - plus that it only uses ~14uA in full operation as opposed to the 10mA
standby or idling current of a 555 timer (that's very important for solar applications like trackers and monitors, or long term unused-vehicle applications).