Gary_P has it right. Both the J13 & the L16 were used.
Out of curiosity, where have you tried for J13 parts & what parts do you need anyway?
Servicing your truck with stock parts is not going to be all that easy & my suggestion is to buy yourself a rusted out Series one 910 Bluebird as a donor vehicle & transfer the engine & five speed gearbox from that. I didn't mention the Series two as they have a lot more smog gear to wory about & the Series three with the single cam CA engine, well, we don't talk about those as most people regard the L series as a better proposition.
To make this all work you will need a suitable workshop & a reasonable degree of mechanical knowledge & skill. A Bluebird
workshop manual will be a big help too. If these things are not available to you, then you just might be pushing poo uphill with a pointy stick to do it.
The advantage of buying a whole donor car is that they are often cheaper than just the parts separately, you get everything, including wiring harness, radiator, engine mounts, tail shaft etc. etc. & the L20B is a proven & sturdy workhorse that should fit the chassis without overmuch drama.
If you have the skills & the workshop, then the conversion will be a worthwhile & very cost effective job.
P.S. The J series engines were derived from the old Austin A40 engines, but with everything fixed. They are a basicly good engine, but really should be avoided for anything but a restoration since there are engines available that are so much better for so very llittle money.