This is a self-answered question, as encouraged on Stackoverflow for sharing knowledge. As such, it is a follow-on to my previous self-answered question regarding accurate computation of the principal branch of the Lambert W function, W₀. For some general background on the Lambert W function, please see there. When I initially looked at the Lambert W function, the negative branch W_-1 did not seem particularly useful to me, but I have since come across a number of publications that make practical use of it, for example ^{[1], [2], [3], [4]}.