"You and your spouse lived apart all year." ' Taxpayer did not live with spouse at any time during year"

I'm looking for an IRS cite or caselaw. defining "living with" or "living apart"

I have 2 similar situations. Retired seniors; 2nd marriages; in one case  2 condo units in the same building (different floors); in another separate free standing residences next door or down the block from each other. The couples legitimately maintain and live in their respective residences separately. But they do spend, a lot of time together, etc.

In each case MFS will result in lower taxes.