Treating security questions like passwords and saving them in your password manager is correct, but make sure that your fake answers aren't autogenerated nonsense like ":s^Twd.J;3hzg=Q~". Many password reset flows involve communicating a security question over the phone, and it's easy enough for an attacker to guess "oh, it's just a bunch of random characters lol" and for the phone rep to just laugh and shrug their shoulders and let the person in. Make sure it's a sentence that makes sense (I would even avoid non-sequitur passphrases such as those generated by diceware), while also making sure that it has no relationship whatsoever to the question.
Will probably work about as well as that time when I was young and decided to spend about a week signing all receipts with a signature that looks nothing like my usual one, just to see if it would ever be challenged.
Many people are, contrary to all pretense, mostly paid to not give any actual fucks.
What do you think the signature is for? If a store can provide a signed receipt, the bank eats a chargeback. If they can't, the business pays. No one verifies that it is your signature. It is just an anachronism of how contracts work.
My password generator (or just do it manually) can generate word passwords like correct-horse-battery-staple using real words, which is probably a bit easier to read over the phone.