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I'm not an SC Guru...but from what I can tell in the SC instructions (TN Has no individual income tax)

As long as you maintain a separate, essentially full-year domicile in TN, even if you go back to SC occasionally   (i.e. you are not there in TN on a temporary basis, ) , and that your wife both works and lives only in SC....essentially full time, ignoring occasional weekends or vacations.

Then:

From the General instructions for SC...you have the choice of filing both Federal and State forms as married-filing-separately (MFS), where you create separate Federal form for each of you, and then just an SC-MFS form for her (assuming you-yourself have no SC-source income).   And if you do have some SC income while back in SC, then you also would also file a separate MFS tax return, as an SC Non-resident, reporting just the SC income.   TO do both the MFS-Federal and MFS-SC tax returns would require you to either use entirely separate "Online' TTX accounts, or use the Desktop software, which allows you to create separate MFS-Fed&SC files for both of you.

 or....filing joint (MFJ) for both Federal and SC, but using the Schedule NR in the SC forms to enter whatever $$ you (the non-resident spouse) earned while living in SC.

In the following General instructions for SC....you are the spouse who is not a SC Resident

"How should I file if I am a full-year South Carolina resident but my spouse is not?
If you file a joint federal return, you must file a joint SC1040 with the Schedule NR. You will report all
income for the entire year to South Carolina. Your spouse will only report income earned in this state.

If you file separate federal returns, you must file a separate South Carolina return. Your spouse must
also file a separate South Carolina return if they have income taxable by South Carolina."

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However, if you might be considered an SC resident...because you are expect to be in TN temporarily (perhaps one year or less and not returning to TN after working there 8 mos), then you might need to file MFJ-Fed and SC....and report ALL your TN income as being SC-taxable.

SC General information says the following:

"Am I a resident or nonresident?
You are a South Carolina resident, even if you live outside of South Carolina, if all of the following are
true:
1. Your intention is to maintain South Carolina as your permanent home.
2. South Carolina is the center of your financial, social, and family life.
3. When you are away, you intend to return to South Carolina.
You are a nonresident if your permanent home is outside of South Carolina for the entire year and
none of the above applies."

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IF you have any question about whether your tax domicile is truly in TN, or SC, you might need to see a local tax professional in SC to discuss the details of your work-living relationship for now and how you both expect to live-work for this, and the next few years.