Just so you know, the difference between a Singer 66 and a Singer 66K is the same as the difference between a 99 and a 99K, or indeed a 201 and a 201K i.e. nothing. Zilch. Nada.
There is no difference at all. All that “K” suffix does is tell you that the machine was made in Singer’s Kilbowie factory in Clydebank, Scotland.
At one time, Singer had factories all over the planet making basically the same models, so depending on where it was made, your Singer Model 15, for example, could be a 15K (Kilbowie), or a 15E (New Jersey), a 15A (South Carolina), a 15SJ (Quebec) or perhaps even a 15P (Podolsk, Russia). And even if you had one of each of those, you still wouldn’t have a full set.
What there is a difference between is machines with different numbers after that suffix. Those numbers tell you what the variant is, for example a 201K1 is a natural-born treadle machine, whereas a 201K3 is a portable (or more accurately where the 201 is concerned “portable”) electric.
So there you go. The “K” just means it’s a home-grown Singer.
Get into model numbers any deeper than that and you’re entering anorak territory …