pumping the pedal works in a pinch, but we do not recommend this practice whatsoever.
The reason for this is you're forcing the piston to travel way too far and this could potentially tear the seal in the master cylinder. You're really sh!t out of luck then, and you're left with a leaky system and more money out of your wallet to replace.
You really want a setup like this:
MityVac 7400 - Fluid Evacuator - 7.3 Liter
I use it religiously for all forms of brake bleeding/clutch bleeding. It contains the mess, you don't have to keep pumping, and the best thing is that you don't damage your system.
The money you spend on this setup, is time saved but also FLUID saved from constantly pumping and second guessing and ending up with a crappy feeling pedal. Do it once and do it right.
Also, in the USDM manual, the proper bleeding process begins with the driver side, in our case, LF then RF, RR, LR.
The ABS system is designed to be bled this way. I suspect it MIGHT be counterclockwise starting from RF for the RHD guys, due to where the master cylinder is placed. Can anybody with the factory service manual confirm this?
Brake lines do wear out, but if you're experiencing a soft pedal, it's most definitely air in the system still. If it's the brake lines causing the soft pedal, you've got a crack and a leak/bulge....very very dangerous!