Your solution looks elegant, and this one is kind of clunky, but it does have a delay…

https://www.banggood.com/12V-Car-LED-Running-Light-Relay-Harness-DRL-Controller-OnOff-Switch-p-934191.html?rmmds=cart

Also from banggood but less ‘kit’ than the one Alistair posted, and without the adjustability/LED readout aspect.

You could, however, wire it in to the circuit that controls the door lights and tuck it up under the dash. 

Or, use it for what it is meant for - daytime running lights!

…r