What element or module do I need?

Question

Electronics

It is necessary to implement the following:
There is a button, when pressed, it closes the contacts to the further circuit of the first consumer (a regular switch, but without fixing, as on a bell).
It is necessary to make sure that when you press more than X seconds (the time must be adjusted from 1 to 5 seconds maximum), a signal appears on the second button of the same type, but without pressing it, it goes to the second consumer, so to speak, directly, at the signal of the first button and passing time span.
Mains voltage 12V.

Answer 1

this is called a turn-on delay relay.
google the scheme or buy on aliexpress.
https://www.aliexpress.com/item/32877105138.html
https://www.aliexpress.com/item/32801536315.html
or support the domestic manufacturer https://www.12vi.ru/766/894/
I don't see in the text, the shutdown algorithm, perhaps you need to think about how to turn it all off later.