Possible camshaft ID 360 street build

Duration is 250, by itself means almost nothing. It needs to be accompanied by a spec, like "@.008 tappet rise"; or "@.050" , and if it is the intake or the exhaust duration.
Now in your case, you also provided the lift of .488
Together, these two numbers can point us to a possible cam, but it would just be a guess, into a family of cams.
My guess is that, if a solid lifter cam then she is about 284 Intake advertised duration.
if a hydro, then possible closer to a 292@ advertised.

But if that 250* you mentioned is the advertised, then it is about the same size as a 360 2bbl cam.
So then to tell the difference, you gotta hear it slow-idle at around 700/750. The 2bbl cam will make big vacuum and idle dead smooth with no lope.
The 250@ advertised will have a pronounced idle-lope, have vacuum closer to 10/11inches, and be a lil rough depending on how well it was tuned.

if a 292 hydro cam, that's a pretty big streetcam for a car with an automatic......