here's a new one for me. Signature Guitar Company. Now out of business.
Per a historic discussion web page at: http://www.geocities.com/signatureguitar/
it is said "Neck through Signature guitar bodies were crafted by luthiers from "Larrivee" 1987 thru 1990.
There's a bass with a Signature bridge plate and Larrivee headstock currently on ebay which started me down this path.
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Might be a frankenstein. Larrivee neck on a Signature body. Hey, wait a minute, I think I saw one of those at Sid's house in Toy Story! :SHK>
Until recently, some dealers in the UK were stocking a new range of Japanese guitars bearing the name 'Signature'. I don't think there's any connection with the Canadian company you're referring to but all the same they seemed to be pretty decent Les Paul clones sold at a reasonable price.
The bass's headstock is unlike the later pointy heads. I'll note the logo is the very earliest Larrivee scripted style logo, circa 1983. This may be one of the very earliest electrics from JCL. However if Signature was in business 4 years later, then my guess is that the bass has a replacement bridge plate/cover. Or the bass sat unfinished at Larrivee and was later completed when Larrivee started furnishing bodies to Signature.