If you are completely off the beaten track on a route with no regular pilgrims and you have a non breathing casualty, your options are pretty limited. Has the casualty got a pulse? No, then they are dead. Do nothing except mark the spot and go find a way to contact the local constabulary.
If they have a pulse it gets more complicated, but if they had say a heart attack, your chances of reviving them are pretty slim without an AED and medical assistance, so you can try breathing for them, but if they fail to come around within say 20-30 mins, you will have to make a decision whether to continue or allow nature to take it's course. You can not provide CPR indefinitely. People talk about giving CPR for an hour, but that is like running a marathon. If you have no signal or way of alerting emergency services, that person is unlikely to survive.
Unconscious, but breathing, put them in the recovery position, give them some shade and try and find help or call for help. If you were strong enough you could try carrying them to somewhere more accessible, or where you are more likely to find help, such as a road, but for safety, I would put them in the recovery position. Also have a quick look through their stuff, find out if they have any tablets or insulin. That info will be of use to the emergency services.
This situation can be planned for, but in reality it is something that can only be dealt with in the situation. Use common sense if you ever come across this sort of issue. First aid training is also useful, advanced training if you have it can be really useful too, but it's mostly only undertaken if you were training as an Expedition Leader or Mountain Guide, at which point having a ticket in Expedition Medicine is useful.
As Tincatinker suggests, trying to call 112 is your primary goal, no matter what. But even if you do get through and arrange help, if you are half way across the Pyrenees or even at the Cruz de Ferro, it isn't going to get there in 5 mins. You need to keep your casualty alive until it does get there, if you can. In the UK they will guide you through how to do that, but I don't know if the same would happen abroad. If they tell you they have sent a helicopter (and you are able to) then get any rucksacks and bright clothes and make a visual marker to help them locate you. Which Three Words App should be used if you have it.
Sorry, no easy suggestions on this topic. It was covered on a work related first aid course I did and it's a complicated subject. My work is mostly remote and often solo, so being able to deal with any problems I or the team I operate in might encounter, is really important. On some Camino routes, the same might apply. But it is something to learn through training.
Praemonitus praemunitus.
