This might be a weird question but can academic writings be a source of unwritten law like customary law ? And do things like customary law and something like this require a judiciary to interpret or deduce it ?
In practice, common law courts turn to academic writing, either law review articles or legal treatises or the "Restatements of Law", on a regular, but infrequent basis. These sources are not binding sources of legal authority but can shed persuasive light on the logic behind a legal rule or the course of action that has been taken in previous similar cases.
In civil law countries (i.e. those not descended from the legal system of England), there are far fewer circumstances in which court precedents are sources of law. Much of the gap in credible sources for how ambiguities in the statutory law should be interpreted in these countries comes from academic writing. In a typical civil law country, a leading law professor has more impact on how the law is interpreted than senior appellate court judges. Again, academic writings are not binding legal authority, but in the absence of alternative sources for material interpreting statutes, they are very persuasive.
In Shari`ah law, there are two authoritative sources of law, the Qur’an and the Ḥadith. However, sometimes things are not crystal clear, and there may be need to engage in legal reasoning beyond taqlid which is precedent based on “consensus” (ijma`). In that case, a legal scholar may be required to engage in ijtihad, i.e. legal reasoning. Such a writing cannot (by definition) be authoritative, but it can be persuasive, in that it might be relied on to resolve a case.