A few identifiers
It's hard to determine if a particular vehicle was made with a specific engine or not for that year Chevy. The cowl tag will not tell you which V8 was original to the car, but it will tell whether it carried a six cylinder or a V8.
If you are so lucky as to have a well preserved 1962 Biscayne that has what you believe to be the original 409 engine in it, then the detective work gets more interesting. First, there's a different fuel line, both in diameter and in pattern, for the 409 (as opposed to the 327/283/235). There are some additional telltale signs, including a ballast resistor on the firewall, and some other items others can mention.
If you show us some pictures of what you have under the hood we can give you some advise. Here are a few facts that we know of the 1962 409 engine:
Came in two builds, one single 4 barrel setup with 380 horses, the other a dual quad setup with 409 horsepower. Unless it was a truck engine from that year (then it wouldn't be considered original, would it?) it had high perf 690 heads and an aluminum intake with one or two 4 barrel Carter AFBs. The casting on the rear of the block (near the bellhousing on the driver's side) should end in "068" and there will be a date code to its right that indicates when that casting was made. If it was made before the build date of your vehicle, that's a good sign. You can estimate the build date of your car from the cowl tag, which denotes things like body style, manufacturing plant and sequence number (along with interior and exterior paint codes and some accessory codes).
If your car was originally an automatic, then it wasn't a 409 car. These had four speeds and perhaps in some cases, a three speed transmission. Most were T-10 four speeds in 1962. Some say the tachometer was standard with performance engines that year, so look for that on the steering column. There are other signs that we might be able to help you with.
So, let us know what you have in place and we'll try to help out as best possible. It's not terribly difficult to "clone' a 409 into a '62 and make it look correct, so beware of that. The 409 could reportedly be ordered for any passenger style body, so having one in a Biscayne, while rare, is not impossible.
I hope you have what you are looking for. If not, drive it and be proud of what it is
.
Others will chime in and add to what I've started to identify.
Best,
TomK