Step 1: Recall the functional column. The special visceral efferent column drives the striated muscles that develop from the branchial arches, such as the muscles of mastication, facial expression, pharynx, and larynx.
Step 2: Identify the members. The nerves containing $SVE$ fibres are cranial nerves V, VII, IX, X, and XI.
Step 3: Separate nucleus from nerve. Among the options, the trigeminal, glossopharyngeal, and vagus are SVE nerves. The nucleus ambiguus is the source nucleus of SVE fibres for IX, X, and XI, but it is a nucleus rather than a nerve, so it does not belong in a list of SVE nerves.
Step 4: Conclude. The exception in this set is the nucleus ambiguus.
\[\boxed{\text{Nucleus ambiguus}}\]