I agree with all the above posts, including Saddleman's admonition about solder joints being at increased risks for fatigue fracture. That said, many of the cheaper crimp connectors will oxidize over time and the circuit may become "flaky" due to varying resistance or open circuit. A properly soldered connection is excellent as long as the joint is isolated from vibration. A quality crimp connector can also be an excellent connection if done properly and protected from oxidation with dielectric grease. The non-soldered crimp connection is a better choice where the joint cannot be isolated from movement.
Solder joints should be stabilized to prevent flexing. The wire gets brittle from the heat during the solder process and can eventually break right next to the solder joint if flexing occurs.
What you have pictured will work.
I prefer heat shrink tubing for insulation over liquid tape or wrapped tape. I would have cut the OEM wiring right through and slid a piece of heat shrink tubing onto one end of the cut wire far away from the intended solder joint so the heat of the soldering process wouldn't affect the heat shrink tubing. (make sure the section of heat shrink tubing is long enough to overlap the wire's insulation on both sides of the solder joint. too long is better than too short.)
I would then strip the ends of the OEM wiring and twist them together along with the wire being spliced in. If additional length were needed because the existing OEM wire was run so tight that a half inch of overlap of the original wire ends could not be obtained, I would not hesitate to splice in a short length by stripping the wire being spliced in for a greater length to close the gap between the OEM wire ends.
After twisting the wires together for a good mechanical connection, solder a nice shiny connection. Too little heat or movement of the joint before it cools will cause the solder to be dull; referred to as a "cold solder joint", this will lack good electrical conductivity and be mechanically weak. Too much heat will unnecessarily weaken the wire adjacent to the solder joint, increasing brittleness, resistant to current, and breakage. Unnecessarily "cooking" the wire during soldering will increase resistance in the wire and depending on current loads, over time that increase in resistance will result in current continuing to "cook" the wire.
Once the joint is soldered, the heat shrink tubing is slid over the joint and mild heat applied to the tubing to shrink it.