How and where woud you start a new ball of yarn when both edges will show in a cape?
For me it would depend on the pattern and where it would be the least obvious.
I start the new yarn when I run out of the old one. I tie the ends loosely, then work a few more rows an rearrange the knot so it’s the back of a purl bump on the WS row and tighten it, then weave the ends in. Or you could use the Russian join for a knot free looks like one piec join. There’s a video on the Tips page, I think.