Sign in to manage apple ID
Go to "Password and security"
---> at this point you may be able to change your rescue email address
---> you may need to answer security questions and THEN be able to
Alt strategy --
This is what I actually did when I needed to change my rescue email. However, it is clear that the above strategies would now work for me.
I needed to change my rescue email b/c I wanted that email to be my primary email/appleID. The rescue email and primary cannot be the same for some reason. When I needed to do it, I forgot the answer to one of my security questions so was forced to click "Send reset security info email to •••••@***.com." This sent an email to my rescue email address -- so if you cannot access your rescue, this alt strategy will not work.
When I clicked the link sent, something went wrong and aple could not bring me to that page. However, when I looked back in the browser tab where I was managing my AppleID, the page/environment for "Password and security" changed. All that was there was something to click that said "Reset .....". This brought me to a page to change all 'password and security' related issues including my rescue email address.
Summary of Alt:
Sign in to manage apple ID
Go to "Password and security"
click "Send reset security info email to •••••@***.com."
--> may have to go to rescue email address and follow instructions there and it may work
--> could be you only have to renew the 'password and settings' page to see new option to click "Reset...."
--------> This latter step was available to me after clicking link in rescue email