What you hear is right. The NJME roster is 35 on/31 off.
They fly you in and out from wherever you are based. I think on average you spend 40-50% of your time in Saudi, the rest outside the country.
Not sure which position you'd be applying for and I'm slightly out of touch with the pay scales but last I heard the salary for a Falcon 2000 captain was around the $100,000 mark. Per diems are $100, paid in advance. Contract typically three years with a loyalty bonus if you stay the distance.
They also have Hawkers and Gulfstreams. No idea on salaries.