
Your question quite has the answer in it. The period that you have to wait before you can evict a person depends on the terms of the contract that parties to the contract have agreed upon.
Any land contract will also include the payment date and the other terms and conditions that the parties have to abide by. In that case, if the person fails to honor his commitment with the said period, the victim can always evict the person.
Once the dare falls due, you are good to evict the other person.
However, it is your personal choice to extend the process of eviction if you choose to or based on the promise of the other party that he will honor his committed on the extended date. It is again better that you get it in terms of writing or you better evict the person.