Are Common External Tariff levels decided by qualified majority in the Council of Ministers?
Or are these classified as taxation and therefore need unanimous agreement?
"Unilaterally" doesn't apply here, as I would argue there is no such thing in EU. I am not certain if "unanimous" does, but it doesn't look like it.
CET tariff levels are EU regulations. EU regulations are "a form of EU secondary legislation, used to implement objectives under EU law." https://europa.eu/european-union/eu-law/legal-acts_en
The method for changing tariffs therefore is amendments to existing EU regulations, which generally follow Ordinary Legislative Procedure:
[...] Via a series of readings of a proposed law, Parliament and Council review and amend the text. If the two institutions agree on the amendments, the proposed law is adopted. If the Parliament and Council cannot agree on amendments, a second reading takes place. If no agreement is reached at the second reading, the proposal is put before a ‘conciliation committee’ made up of equal numbers of Parliament and Council representatives. Commission representatives also attend the meetings and contribute. Once the committee reaches an agreement, the text is sent to the Parliament and Council for a third reading, so it can finally be adopted as law. On the rare occasions where they cannot agree, the law is not adopted.
However, I found only unanimity definition for European Council, not EP:
The Council has to vote unanimously on a number of matters which the member states consider to be sensitive. For example:
common foreign and security policy (with the exception of certain clearly defined cases which require qualified majority, e.g. appointment of a special representative)
citizenship (the granting of new rights to EU citizens)
harmonisation of national legislation on indirect taxation
EU finances (own resources, the multiannual financial framework)
certain provisions in the field of justice and home affairs (the European prosecutor, family law, operational police cooperation, etc.)
harmonisation of national legislation in the field of social security and social protection.
In addition, the Council is required to vote unanimously to diverge from the Commission proposal when the Commission is unable to agree to the amendments made to its proposal. This rule does not apply to acts that need to be adopted by the Council on a Commission recommendation, for example, acts in the area of economic coordination.
It appears to be subject to qualified majority voting by member states, through the "ordinary legislative procedure". This explainer seems to be good:
2.26 With the exception of Article 31, all the Treaty articles cited above have direct effect. That is, they are in themselves law in all the Member States and national courts must not only apply them but give them priority over any conflicting provisions of domestic law. In addition, the EU has power to legislate both on the Single Market and on the Customs Union. The EU’s power to legislate on the Customs Union is exclusive (Article 3) while its power to legislate on the Single Market is shared with Member States (Article 4).
The ordinary legislative procedure is the legislative process which is central to the European Union’s decision-making system. It is based on co-decision; joint agreement by the European Council and European Parliament, and QMV. It is based on the principle of parity and means that neither the European Parliament nor the Council) may adopt legislation without the other’s assent. Any differences between the European Parliament and Council may be resolved within a conciliation committee where both sides seek to agree a joint text.
So the combination of Council (the leaders of the member states) operating with QMV and European parliament can, together, agree to change the CET. Once this decision is made it cannot be vetoed or ignored by individual member states. I would not describe this as "unilaterally" - it's extremely multilateral!