It’s a late 80s early 90s (S13 chassis) 240SX/200SX/Silvia (depending on locality) with a front end conversion to late S14 sheet metal. Uncommon modification but not unheard of. Originally it looked like this.
HA! and HA! AGAIN I SAY!
I had to drop off some parts for shop work today (front strut assemblies, my spring compressors just would not work to get them apart) and there in the shop parking lot was the mystery car of this thread.
It’s a Datsun 260Z convertible conversion with some other custom body work and nary a badge or label anywhere on it. Got some pix, and you can see why it was so confusing - it has all the details discussed above but doesn’t add up until you can get a good look at the tail lights and headlights.
Ha.
Well, except the big V8.
Wow! That would be a toughie to ID. Congrats on solving the mystery.
My Brother has a Jensen Interceptor convertible. Had Jensen updated / tweaked the nose for more enclosed headlights and chiseled the grill a bit it’d be uncanny cousins with your mystery car.
I would not have put that down as any form of Z-car. Despite the fact I was a college kid in the heyday of 240s and 260s and would gladly have had one if I wasn’t already up to my ears in another marque.
It’s not stock but I’m not sure what’s in it. It is not a Datsun I-6. It rumbles. Google the Scarab conversions of the Z car.
You can stuff a 3.8l = 231CID Buick V-6 into darn near anything. Using 1980s tech those can be hopped up to 250Hp and still be quite drivable. Much over 300 it gets too racy for the street.
It lopes at idle differently than a V-8. But it still sounds way out of place coming out of a Datsun. Or a Porsche like I had at the time. 
I’m glad you found it and were able to make a positive ID. That can be nigh unto impossible with a one-off custom job.
The headlights are an immediate giveaway, but the rear looks more like a TR6, except those are 260 taillights. How the heck did they convert the rear hatch of the 260 to that trunk so seamlessly? Very confusing, but it’s some great body work.
Did you meet or talk to the owner?
Wow, that is an interesting and unique look. I can see why this threw and bugged you. To me the front 3/4 view says Jensen, and the rear lights say Z.
This would’ve bugged me too. You could’ve tortured us and just posted the pics without the explanation. That would’ve thrown me.