Good link, the adapter shown even calls it out as 5/8-18. If someone else has a spare one of these, take it to someone with a thread pitch gage and have them check the pitch and measure the OD. You might find them to be 18 threads per inch with an OD of 0.62. Look in any machinist handbook and you will see that BSPP and BSP are 19 threads per inch. The adapters have roughly 3/8" of male thread so it a close call. All and I mean all of these that I have pulled from heads have measured with an OD slightly smaller than 5/8”.
I use BSPP in my work, having both taps and using them very commonly leads me to stay with 5/8-18. BSPP is used in some vacuum cups; the packaging industry uses them for pick and place of product. A BSPP would be very tight indeed. Hey call or email the guy’s in the link, what do they say?
Dug