Principle Sensory Nucleus of the Trigeminal is located in the Pons, as is the Motor Trigeminal Nucleus of the pons. This presentation is probably dealing more with the Principle Sensory Nucleus.

The pons has nerves 5-8, so the trigeminal would be affected here

The mnemonic I like for remembering the locations of the cranial nerves is the "2,2,4,4 rule"

Above brainstem= CN I + II Midbrain= CN III, IV Pons= CN V, VI, VII, VIII Medulla= CN IX, X, XI, XII

I do understand that the principal nucleus of the trigeminal nerve is located at the pons. But since this patient is having trigeminal neuralgia wouldn't you be disrupting the pathway involved in pain and temperature, which in this case would be the spinal nucleus (located in the medulla)?

Besides, I found this at an article

A recent hypothesis attributes the pain of trigeminal neuralgia to a central mechanism involving the pars oralis of the spinal trigeminal nucleus.[5]

https://www.ncbi.nlm.nih.gov/books/NBK539729/

theres an association made in 2017 with trigeminal neuralgia and MS - which is what i think this pt has. key thing to note is that while all motor and sensory fibers of CN 5 enter at the level fo the pons (however some also do enter at the level of medulla and even the sc via the spinal tract of 5 to synapse with the long sensory nucleus of 5) heres the link of trigeminal neuralgia and MS: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5649347/

I was thinking along the lines of facial sensation which is mediated by the trigeminal nerve and the fact that the trigeminal nerve is located in the pons.

MS is a demyelinating disease. That's why I didn't pick cortex or thalamus; they are grey matter. I picked medulla because I the spinotrigeminal nerves traverse the medulla. I guess we are just supposed to assume the demyelination is happening in the pons? I don't know.