I know a 12JP4 is shorter than a 12LP4 (maybe because it doesn't need a trap?), also a genuine Dumont 12JP4 is a lightweight tube with a thin somewhat rounded face, possibly Pyrex glass, and the envelope is shaped somewhat differently, also the anode connector is different having a small ball inside for the connector, the 12LP4 is heavy and has the usual thick flat face and just looks like a bigger 10BP4.
That said I have an unmarked tube that is supposed to be a 12JP4 but it looks like a 12LP4, it doesn't use a trap though and it has an Ion burn just like most of the non-trapped 12JP4's
If you Google the numbers you will find some PDF's with the data for both.
The ETF has a picture of a real 12JP4, if you look closely you can see it's more rounded and there's a bump where the neck meets the bell.
http://www.earlytelevision.org/postwar_crts.html