There is no way to find the salt other than trying all possible guesses and checking the result. Although PBKDF2-HMAC does not treat the password and the salt in the same way, it has the same essential security properties with respect to both.
If you know the password (passphrase, mnemonic words, whatever you want to call it), and the salt has low entropy, then the derived hash is guessable, just like if you know the salt and the password has low entropy.
The salt is typically not indented to be secret, because it has to be stored. A non-secret salt doesn't have to be unguessable, it only needs to be mostly unique, because the point is to make it not worth the effort to do mass precomputation of PBKDF over common passwords. However, if you do have a place to store a secret securely, then making the salt secret is a bonus, and then you should make it high-entropy. A secret salt is typically called a “pepper” (but often the pepper is shared between multiple accounts whereas the salt is public but per-account; a shared pepper can't be a salt on its own). Regardless of how the salt is stored, taking a random salt is both easy and cheap, so there's no good reason to not have a high-entropy salt.
P.S. ~2000 iterations is ridiculously small. OWASP currently recommends ~100,000 iterations for authentication, and key derivation should use more iterations than authentication because it can be done offline without a time constraint (whereas for authentication, the attacker has to first breach the database and there's a chance that users can update their passwords if the breach is noticed).
