Oh yes, Parnet cables are special, as ACKnowledge and SELect are bridged together locally at each end, if I recall correctly. They most certainly are not null-modem, which is only suitable for serial port connection. Instructions for making them are included in the original distribution archives.
I personally would not trust any such cable bought from an uncertain source on eBay (and the fault might simply be a bad or loose connector pin). I made my own adapters (which plug onto each end of a universal 25-way straight-through extension cable) and I recommend that you do the same unless someone such as Amigakit can supply a guaranteed correct cable. Making a Parnet cable (or adapters) is not hard or complex, but you must be sure that you have them wired properly. Use of a wrongly wired cable might damage the computers.