When I bought my house, I inherited a fruit cage with raspberries in it. No labels - not a clue! I have pounds and pounds of the things. i have never done anything to them and I have always had a "thicket"! Apparently, there were both summer and autumn berries, but I treated them both the same cutting them right down every year and not leaving any growth and they come back every year, and supply me with fruit for months and months. Now I know this is ot supposed to happen - but I assure you it does! So my advice is "go with the flow"
Ps I have planted a new fruit cage with some (carefully labelled) raspberries and I plan to do it properly if I can in at least one place!