Louise, since you KNOW that you are dealing with an old sink and not a fiberglass or composite material, you can strip with something like Citristrip. Use a plastic putty knife for removal of the old paint and stripper goo. Let the stripper do the work but don't let it get dry and hard before removal. One tip is that you can carve the plastic putty knives to any angle or curve to help you remove the goo from problem areas. Don't forget eye and skin protection and be careful about getting stripper on other paint in the area.