If I break the option amount due in two parts with second part due in 30 days, is non-payment on the remaining option balance from the t/b grounds for eviction?

It would depend on how you wrote the money due into the contracts. More likely non-payment of the remaining Option Money would void the Option to Purchase, NOT the Lease.

If you are going to accept payment(s) on the Option Money, write a separate Note for the amount due.

Kimberly-

Thanks for the reply.

Have you ever used any language to tie both agreements together where nonperformance on the option equates to nonperformance on the lease?

Or maybe someone could share what they have done to address this type of situation...

Caveman, if they only get 30 days to come up with the second part of the Option, why not just have their move-in date after that point? They are going to need to give their current landlord 30 days notice anyway!

Caveman, a bigger factor in the consequences of nonpayment of the option consideration would be your state laws concering this, more so then what you write in a contract.
Personally, if I were to be collecting, say, $2,500 option money today, and the balance of $2,500 in thirty days, I would do as Kim said and tie that second payment into the option to purchase, rather than the lease agreement. From a legal standpoint I think you'd be on stronger ground setting it up like that.