Unfortunately, there isn't any medical evidence that a capsacin patch on the skin would help with the pain of trigeminal neuralgia. However, that doesn't mean it won't work for you, and it is certainly something that is relatively low risk, that can be tried to see if it helps with the pain.
Traditionally, the medications such as tegretol and baclofen are often used as the first line treatments, and the other medications for nerves such as the lamotrigine, and the Lyrica.
There are potential surgical interventions as well, and can include surgical microvascular decompression (which helps if there is a blood vessel pushing into the nerve, which is apparently not there on the MRI, though the MRI can miss some things). Rhizotomy and gamma knife surgery can also be of benefit.
So discussing with your doctor about all these issues would be helpful, and they can help to prescribe this capsacin cream for you to try if you'd like.