Simple timed controller

[solvejskovlund]

I'm looking for a circuit to control a relay using preferably a single button, but two buttons is ok.
I picture a behavior similar to this, starting with the relay control signal off / disconnected / floating:

case 1:
Press the button once: power on the relay, set a timer to X minutes and start count down.
When time runs out, the relay control signal is turned off.

case 2:
Press the button: power on the relay, set timer to X minutes, start count down.
Press the button again: add X minutes to the timer.
For every press on the button another X minutes is added to the timer (guess there should be a max of an hour or two)
When time runs out, the relay control signal is turned off.

Additionally there should be a way to reset timer to 0, power off before the time has run out.

Also I'd like some kind of indicator that indicates the reminding time.

I wouldn't be surprised if a circuit like this exists like a mass produced pcb, or maybe even like a device with a box. But I can't find any. What would be the proper search terms to find such a circuit?
(I've found premade PCBs that has an time setting that can be controlled by multiple buttons, and a main button that starts the timer. But repressing the button either turns off or resets the timer to the initial first press time. They do not extend the time by pressing multiple times.)
The usage of this is lights in a half open shelter. Motion detection lights switch does not work because of animals, and I want this to be controllable with a foot switch cause my hands are usually full when I need to operate this. )

 

[Borek]

Pretty easy to build using any programmable microcontroller. Start with an Arduino, as it is cheap and probably the easiest due to tons of tutorials.