Interesting post, interesting brand.
When I grew up in the 70's, Sigma was a quite a common cheap guitar brand here in Sweden. Lots of acoustics, but also many Japanese-made electrics, your standard copies of the usual suspects, Strats, LPs, SGs etc, almost as often seen as Ibanez and Aria.
But when I started taking an active interest in MIJs about a dozen years ago, I found very little info about Sigma electrics, and what little that came up mostly concerned the weird, early-70s, apparently Tokai-made semi-copies of Teles, SGs and P-basses which were also sold under the Ampeg brand (Big Stud etc) for a while. If not, the guitars concerned were almost always sold in or posted from Sweden.
I looked into it closer, and it turns out that Sigma (usually in caps, along with the sideways M sigma symbol or in an oval) was used as an importer brand by Swedish guitar manufacturer and distributor HC Levin during the 2nd half of the 70s and until they folded in 1982. And yes, there's a CF Martin connection there, Levin having been acquired by them in 1972 (apparently mostly to get at their stock of woods). It seems they borrowed their parent company's brand for their own importation of low-end/mid-level Japanese guitars for the Swedish market.
The origin of the guitars is a bit murky. So far, I haven't been able to get a really close look at any of them, but I see no real evidence of any Tokai connection. I'm not sure if that's even to be expected if we're talking say 1976-82 or so. I've seen some possible Fujigen builds, some seem more likely to come from low-end specialists like Kiso Suzuki or Matsumoto Union/Chushin, but I really can't say.
Some pics of the guitars I'm talking about. All are from Swedish sources.