it is a consensual/mutually agreed divorce, without children, or property. The respondent will remain in the same house in the same county - Denton, Texas.
So long as one of the parties appears before the judge to "prove up" an agreed decree, it doesn't matter which one does it. The residency question applies to the time the divorce suit was filed. Once filed, you do not have to remain in the county. You do need to sign the agreed decree and to file it with the court.
I am not intending this to be legal advice, because I don't know the particulars of your situation. Call me if you would like to discuss this or other isues.
At a minimum, at least one party must be present to offer sworn testimony at the final hearing; however, both parties will need to sign the final decree.
Family Law Attorney
Without more information, and without seeing the petition along with (if any) the county's standing orders, it is difficult to provide an answer. Typically in an agreed divorce, either party can do the "prove up" of the final divorce. At least one party must be a domiciliary of the county in which you have filed. You should contact a local family law attorney today.