500 hours per year, even done at 0.62M in a legacy 500-series Citation, is quite a bit of flying for only two full-time pilots. Also, multiple owners means a much greater chance of RONs which will kill your quality of life.
With you being the only insured PIC, you need to find contract pilots that qualify to be PIC (so you can actually have time off) and that you trust (who won't try to take your job), and the owners **need** to understand that the going rate for a qualified, competent light jet contract PIC starts at $600/day plus all expenses and very well might be higher and that they should expect to utilize that person when you or your colleague aren't available.
Splitting management duties is a good idea...but there will only be ONE primary point of contact for the owners, maintenance shops, FBOs, etc. One person who gets called when plans change, the plane breaks, trips pop up where you need to be airborne 30 minutes ago, etc. That person (you, since you're the only PIC) need to be properly compensated for having the responsibility of being the one that catches all the shiat that will inevitably roll downhill.
Sick & vacation days? Don't over-complicate it with an oddball monthly accrual. Both pilots start with 7 sick and 14 vacation days (for example) and leave it at that.