Want to stay stock with 13" tires, but can't get them

And why are we even discussing 185 80 13s? Those are the WRONG size for your car anyway. The original size was 650/13, which equates to a 165 80 13. The 185 70 13 is only .2 of an inch shorter (same size in some brands) but gives you a wider footprint AND is available everywhere. You're just making things hard on yourself lookin for the WRONG THING!
Basically because that's what is on it now. However you could be correct, as I haven't looked at the manual.

According what I did find online and what I believe that I thought I saw with the car, the original size was 7.00 X 13. That equates to 185 80R13. But you have a point and I will double check the owners manual (yes I still have it) and see what it says. I just don't want to get into the issue where the tires rub the wheel wells. I'll see what it recommends and post here.

Where did you come across the info of 650/13 being the original size? This is a Valiant signet (not a 100 or 200) if that makes a difference. It's entirely possible that size was put on the car because of availability and it was a substitute that fit. It was years ago since the tires were purchased, which is why they need to be replaced. If the original size was 650/13, going with the wider tire would be easier.

Thanks for the feedback!

Here's the page from the manual. It a 273 with drum brakes and A/C, so that's why I was looking for the tire size I was. There is lots to take in, and it might be time to get new wheels with the tires and just put 14s on it.

Tire Size from Manual.jpg