No, you do not have to, but most people prefer to pay online when they file an amended return. It is up to you. When you enter the information for your account to be debited and mail in your amended return the IRS will directly debit your account when they process the return.
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Do not include your old 1040 nor your revised 1040 because the Form 1040X reflects any changes there and becomes your new tax return.
The bottom line is, direct debit/direct deposit is not an option with amended tax returns.