MacBook – Should I buy DDR3 or DDR3L RAM for late 2012 MacBook pro 13 inch

Any 1600 MHz DDR3 SODIMM will work. You do not need to buy one from OWC or any Mac specialty shop.

It could be the RAM is just bad. It happens sometimes.

But try to rule this out. Reset SMC and NVRAM(why not?) and boot into Apple Hardware Test to check the memory.

Also you may try to use new 8GB stick paired with old working stick. If it will be OK than don't try to buy same second 8GB stick it will not work. Though it does mean you can use this module with different fully compatible one it's better to send it back.

Anyway I would recommend you are buying DDR3L. It's a new and improved standard your model of MBP supports.