Frank, I'm with d.verry on this one, crimp is usually the better way to go. But offhand, I'd usually take two 14g wires and treat them as one 12g wire (just moving up one gauge size) and then crimp them in a 12g (yellow) crimp.
There ARE special crimp fittings that are actually 12g in one side and 14g or 16g in the other...but don't worry about that. Instead, use the 12g fitting to accomodate the two 14g wires. Then on the other side...either fold over the single wire, or insert a second dummy, so again you've filled the crimp fitting "mormally" with the amount of wire it expects.
The Ancor type adhesive lined shrink wrap crimp fittings are the way to go in the bilge. After heating them, they shrink down and the adhesive flows and you literally will get a waterproof connection. They also are long enough so that you can see they fit well over the insulated part of the wire, just strip enough so the bare portion fills the correct half of the crimp fitting. (Half only, it takes two crimps to seat the two wires, one from each end.)
Pulling on the crimp to test it IS the right way to do it, if you can pull it apart, it was no good anyway. Those cheap hand crimp tools (without the ratchet) can make a workable crimp if you have good hands or you test them. The $50 ratcheting tool is really better--but for one crimp I can understand not buying one.
In our bilge wiring, after I made the heat-sealed crimp AND tested the pump function, I also overwrapped the splice with butyl tape, aka "self amalgamting tape" or "silicon tape" which is a rubbery tape that fuses to itself in 24 hours, forming a second waterproof coating over the splice.
Solder works...but long term testing shows it isn't the best solution even though it "seems" like it should be. Among other things it sets you up for galvanic problems because now there are more metals in the joint, unmatched, and creating a stiff point to work harden the stranded wires.
Take up whatever slack you have from the bilge pump to the splice, and try to hang/screw/whatever that joint as high up as you can. That way, even if the waterproofing fails, less chance of it getting wet.