I got my UK (folded paper) licence inscribed when I was resident in Tenerife. That was prompted by my Spanish stepson receiving a 450 euro fine for not having his inscribed. I don't remember all the details of the process but it was pretty simple and started with a visit to Tráfico in Sta. Cruz, where I just asked what to do and was guided by them. I had to go back a few days later to collect the inscribed licence.
In December last year I got a letter to say my inscription had to be renewed. This involved getting a medical at a clinic in Adeje just down the hill from the post office, and then the rest of the paperwork and payment was somehow done in the PO, but again I don't remember the details (the Alzheimer's is getting a firm hold).
Virtually the next day I was pulled up for speeding. I had been pressing on a bit, but I was allowed to go with a stiff wigging. Whether it was because it was too hard to give me points on a UK licence, or just because I was polite and apologetic, I'll never know.