It's a Centurion Ironman model that I found yesterday (see my intro). The brakes/cables work so I don't think I need to replace them. I'm just wondering how to get them free so I can clean up the rust etc. Do these clips come out of the frame? If not, how to I pull the cable out? It seems stuck in there pretty good. What's the best way to clean up this rust? It's pretty heavy. Lemon juice doesn't seem to be working and it's impossible to get at it with the cable in there. I have a Dremel but I don't want to sand them with cable still in.

Those cable guides are brazed onto the steel frame, and not removable. I suspect that water wicked between the cabl and fitting, and also un the uhderside against the frame, and stayed there to start a rust process.

You need to attend to this before the rust on the tubing gets any worse.

Remove the rear brake cable, and use sand paper, steel wool and/or a chemical rust remover to clean the affected areas down to clean bright metal. Then paint or use a clear paint to make it nier (depending on your aesthetic tolerance.

If you don't attend to this, the rust will eat into the tube at the braze on like a cancer, in which case the frame is toast.

One other option if the fittings are compromised is to carefully cut/file them off, and clean it up down to the tube. Then you can use cable ties to hold brake cables on.

So, I'll probably have to cut the cable. I don't see how it'll come out in one piece anyway, right? Thanks.

If you disconnect the cable at the brake caliber, you should be able to pull it out