-have made this circuit.
When adding 12 v on INPUT, the relay K2 should be activated.
When 12 is removed again K2 is still activated.
When 12v is applied again the K2 should be deactivated.
It would do that except that initial state when power is applied depemds on whether C2 is charged or not. If C2 is discharged when power is applied then K2 will be activated. To avoid this you would need a 'power on reset' circuit.