How to do a Basic Wire Splice
All good advice. I use a "paint stripper" electric heat gun. Works very well, light, and fairly inexpensive. I always double heat-shrink. For critical wet areas like underneath use "adhesive heat shrink" which has a gummy glue inside and seals, but is very expensive. I never use butt crimps. Those seem the mark of an amateur, but usually what you see from repair shops.