SQL unpivot of multiple columns

I would like the following wide table to be unpivotted but only where a user has a true value against the field, along with the appropriate date (please see image for a cleaner version: https://i.stack.imgur.com/9utkN.png).

Current State:

---

CUSTOMER_ID	First_Party_Email	Third_Party_Email	First_Party_Email_Date	Third_Party_Email_Date
40011111	1	1	2021-01-22 04:38:00.000	2021-01-17 06:38:00.000
50022222	NULL	1	NULL	2021-01-18 04:38:00.000
80066666	1	NULL	2021-01-24 05:38:00.000	NULL
_______________	_______________________	_______________________	_______________________________	_______________________________

Required State:

---

Customer_ID	Type	Value	Date
40011111	First_Party_Email	1	22/01/2021 04:38
40011111	Third_Party_Email	1	17/01/2021 06:38
50022222	Third_Party_Email	1	18/01/2021 04:38
80066666	First_Party_Email	1	24/01/2021 05:38
_______________________________________________________________________

Associated query to create table and my attempt that doesn't work:

create table Permissions_Obtained
(Customer_ID bigint
,First_Party_Email  bit
,Third_Party_Email  bit
,First_Party_Email_Date datetime    
,Third_Party_Email_Date datetime
)

insert into Permissions_Obtained
(Customer_ID
,First_Party_Email
,Third_Party_Email
,First_Party_Email_Date
,Third_Party_Email_Date
)
VALUES
(40011111,  1,      1,      '2021-01-22 04:38', '2021-01-17 06:38'),
(50022222,  NULL,   1,      NULL,               '2021-01-18 04:38'),
(80066666,  1,      NULL,   '2021-01-24 05:38', null)

select * 
from Permissions_Obtained

select 
customer_id, Permission
from Permissions_Obtained
unpivot
(
  GivenPermission
  for Permission in (
First_Party_Email, Third_Party_Email
)
) unpiv1, 
unpivot
(
  GivenPermissionDate
  for PermissionDate in (
First_Party_Email_Date, Third_Party_Email_Date
)
) unpiv2
where GivenPermission = 1

--drop table Permissions_Obtained

Any help would be massively appreciated. TIA

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