I have owned this exact same guitar for many years and never knew what it was. I bought it a flea market for $20 and have it hanging on my wall for decoration as it does not play well at all.
I decided to try to look it up and came across this post. This is the only thing about this guitar that I was able to find. Did anyone ever figure out what it was?
Welcome to GuitarZone. This post is a couple of years old, but when it was current I did a little more searching on it. The guitar above was built in the late 60s to early 70s. It was probably labelled "Checkmate" although it was possibly labelled "Teisco" or (less likely) "Silvertone." The actual maker of the guitar was Teisco, a Japanese budget-guitar maker who made their own line Teisco (Checkmate was one of their brands) as well as guitars made and labelled for other seller-companies (for example Silvertone, Vantage (I think) and a few other labels as well.
It's not very valuable. (Maybe $50-$75 if you're very lucky and it's in nice shape.) But they were known for being pretty loud. Most have neck-issues ("Steel Re-Inforced Neck" on a label was just their euphemism for saying "This guitar doesn't have an adjustible truss-rod running through the neck into the neck/body-block like more expensive guitars do."

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However, they generally do have a lot of projection. I don't know what styles you play, but this guitar might be a good one for playing open-tuned slide (like old blues) where fingering the strings is less important and usually done near the nut, and having very high action is actually considered a good thing for slide-work. I have lots of guitars (some cheap and some extremely valuable) and if I'd seen it at a flea-market for twenty bucks I might have bought it myself!
So keep it. Tune it to DADF#AD or DGDGBD and get a slide!
And, again, welcome to GuitarZone.