The timeline I got from Destroying Yemen was that the MB finally fell out with Nasser over his land reform plans in an for Nasser rather uncharacteristically bloody way, and got a place to be terrible in the KSA. That ended with:
1979 Grand Mosque seizure - Wikipedia

The Grand Mosque seizure[7] occurred during November and December 1979 when insurgents calling for the overthrow of the House of Saud took over Masjid al-Haram in Mecca, Saudi Arabia. The insurgents declared that the Mahdi (the "redeemer of Islam") had arrived in the form of one of their leaders - Mohammed Abdullah al-Qahtani - and called on Muslims to obey him. For nearly two weeks Saudi Special Forces, assisted by Pakistani and French commandos,[8] fought battles to reclaim the compound.[9]

After that Qatar became their main sponsor.

I really need to get back to the Curtis book about the UK and radical Islam but I fear I'll have to clean up my desk for this. I'm sure I left it somewhere around here.