I used patches cut from tube for many years with complete success :-

Cut the tube patch round or oval because square corners will snag on things and peel more easily. You can angle the scissors to cut a bevelled edge for a more super patch.

Sandpaper both the tube and the patch very well, that is get through the dirty skin and into fresh new rubber over the whole contact surfaces - this is the key to a permanent join. Even with coarse 150 grit sandpaper it is a fiddly time consuming job.

Apply a thin smear of cement to both surfaces, let them dry for a few minutes, press together.

The normal patch kit patches are 'pre-sandpapered and glued'. The tube still needs to be sandpapered and given a thin smear of cement, let it dry, peel the backing off the patch and press it on.

For a less stressed join, pump the tube to almost the same size as the tyre before pressing the patch on. Doing this causes a tiny bubble to appear in the glue smear, and gives a final check for centering the patch over the hole.