Well, same thing happened to me (@iamUncleMark) and i was able to unlocked my account after 7 days, and i sincerely hope you can unlocked yours by following these steps.
1. Appeal account locked
Contact Twitter via this link https://help.twitter.com/forms/general?subtopic=suspended fill the form, with your full name, handle, email and phone number and explain in details the problem you are facing.
2. Reply Twitter Support Auto response
Now check your email for an auto reply from twitter. Reply the email and tell twitter support in details the problem you are facing.
Hello Twitter Support,
Trust this email finds you well.
My account is currently locked (@ Twitter Handle). I tried verifying my account via Phone Call, when i click “Call me” action bar, it keeps giving me this error ” Sorry, the request failed. Please try again later”
I think there is an issue with the callback service, kindly look into it and unlock my account.
My number: “Your Mobile number”
Attached is a screenshot of the error message. “Attach screenshots of the error message”
3. Logout from Twitter
Now log out your account from every device you are logged into.
Wait for 5-7 days from the day you replied Twitter Support.
5. Login again
Now login your account from a device or a web browser you have not used to access your account before.
This is what i did, and when i click on the “Call Me” after 7 days, the call went through, and now i have my account back.
I sincerely hope this works for you. Good Luck.