In the VIN number:
Model year: C - 1982
Plant code: U - Fujiya

FU won't be in the VIN itself but is in the Model code on the VIN plate

A15 is the 1.5 liter A engine
A15 is the 1.5 liter A engine with Single carburetor

No, this car is a 1982 210 with automatic trans. There is a CU in the VIN. I also have a 1981 210 Deluxe which has the same engine(A15-S) with a 5-speed. It might be considered a MPG version. I have to check the VIN. It has every option that was available being a deluxe. 5-speed, air conditioning, sun roof, tinted windows and a light in the glove box. The problem is that the doors are rusted bad and I've never been able to find door skins.
I was going to ask what the difference is between the A15 and the A15-S ?, but perhaps I'll ask in a new post

Some, but not most 1980-1982 have the Fuel Shut-Off System which sounds like your description.

Is yours an MPG version? This means 5-speed 210s with FU in the VIN.

The 81' and 82' 210s have a vacuum switch that has 3 leads and 1 vacuum port. Also this car has the A15-S engine which might be different. The fuel solenoid is connected to the switch and can't get power without it connected. I think all the older 1200/210 fuel solenoids are connected directly to the ignition switch.

What is this vacuum switch?

MPG 210s have extra stuff on them.

I took apart the carb and tightened the jet. This time when I tried it I couldn't get it to idle unless I cranked up the idle high. I had another carb that was known to be good( a 1979 one),but had similar results with that one as well. After the original problem I eliminated all the emissions stuff, plugged all the ports etc. So after going crazy looking for vacuum leaks, and finding nothing, I finally found the problem.
The 1981-1982 210 has a vacuum switch which is connected to the fuel shut off solenoid. I disconnected it when I eliminated the emissions stuff. My other 210s never had this. So I reconnected it, and it runs great. I was able to get it to idle smooth at 600rpms. I wanted to make sure I posted a follow up on what fixed it. The original problem was the jet not being it all the way , and the second problem with the idle was due to the vacuum switch effecting the fuel solenoid.

Thanks for all the help.

Blocked idle passage somewhere, Quick fix is to swap 1 and 4 plug leads over and rev it while backfiring as that reverse explosion often clears a blockage without a carb rebuild.
The problem is the small hitachis have very small passages that do block up this often works to unblock them

Yes, it needs to be tight.