Does the end of the brake housing that goes into the right shifter need a ferrule? It is a shimano 105 10sp shifter, if that matters.
Yes, you should always try to put a ferrule on a cable housing if you can. It helps keep the housing aligned and helps prevent it from becoming damaged over time.
I’m a SRAM guy, so I’m not sure how the 105 is set up, but if one will fit, use one.