Interesting. I had tried Magic Mouthwash that contained Lidocaine. I could not use it due to the effect on my throat but hadn't thought of it as a dermal application.
Related to where you suggest placing a patch, I tried a peculiar remedy - that after researching why it had temporary effects on tinnitus, by applying to hair and scalp, I decided to test just applying to the back of my neck, lower spine and over temporal lobes. This worked even better. The relief, like the Lidocaine, is temporary. The remedy I used was hot sauce-that sounded really bizarre. But research showed that the reason it works is that it contains Capsaicin which is a neurotoxin to substance p- which is an inflammatory neurotransmitter. The places where I applied the Capsaicin product are where substance p and/or the receptors are most abundantly produced.
(After I wrote this I noticed in the main article that doctors didn't know why Lidocaine worked on tinnitus - I was quickly able to verify that the effect of lidocaine on substance P is well known in field of anesthesiology.)