I replaced the rusty vinyl-coated steel cable lifelines today with 1/4″ Dyneema using Johnson Marine fittings:
Taper the tail:
Bury the tail:
Two different Brummel splices are used. Fittings that are too large to fit through lock-splice are put on first using Brummel lock splice where both ends free. For the smaller fitting that can pass through the rope, a Brummel lock place is used for one end attached. The additional step in the later splice re-inverts the rope after passing the fitting through the tail.