Thanks everyone, for the pictures and initial pointers. I've not had too much of a chance to look at the car per se, I just got it cleaned up after someone left it without the car cover on it in the shop for a while. So the car really needed a bath and polish when my mom called, because it was dirty, that's the first thing I took care, and getting my mom a new soft car cover. Next I want to put it up and change the oil / oil filter / and possibly the air filter, since I don't know the last time any of those maintenance tasks was completed.
This is a 4 cylinder, with overdrive, and no separate opening trunk. The car is blue, as can be seen in my K-F member photo, with a blue interior that's in pretty good shape. I have to look at the car numbers (VIN, and such) because the title (erroneously?) says Henry J, but the closest VIN series I can see for the title matches the Allstate (H330 on title - should it be A330? that's why I have to check the VIN) 4 cylinder, and it has the Allstate badges, radio, et al. Plus my grandfather was pretty meticulous and hated modifying, or buying, modified cars. He wasn't one of the restoration guys that tried mimicking paint drips from the factory or anything, but modification was pretty much a no-no unless absolutely necessary to make it run.
The car does have the turn signal handle, but right now all the lights aren't working. The brake lights definitely function as do most of the running lights. Given the age of the car, and the fact that I've seen 50 year old wires with aircraft, I'm guessing one broke or maybe a relay has an issue. Truth be told, with wiring that's over 50 years old, I might just build a new set of harnesses for the car myself with new wiring so I don't have to worry about random wires deciding to fail whenever they get jostled.
I'll try to get some more pictures as I refurbish the car the rest of the way.
One last thing, the car definitely had hubcaps even when I was a teen, and the spare tire still has the hubcap. Someone, I can't be positive of who, snagged the original hubcaps off the car. I'll get a picture of the one on the spare, but I'm guessing that finding 4 nice replacements is going to be a challenge at best. Any pointers on where to find some, even to refurbish.