It wasn't a grey area exactly, but Roman law doesn't say anything about gay marriage because it was just impossible for two people of the same gender to have a legal marriage.

Of course we should also remember that the concept of being "gay" is really dependent on your own culture, so for the Romans (or Greeks, or anyone else), categories of "heterosexual" or "homosexual" or any other labels aren't really the same as our own. Roman men could engage in lots of behaviours that, for us, would be clearly homosexual. For them the categories were more like active and passive. It was acceptable to be the penetrator and you could penetrate all sorts of other people who weren't your wife, especially if they were lower in status than you. No one's going to think twice if you're having sex with one of your male slaves, but another free man's wife? Not good! A prostitute? Maybe acceptable, but maybe not, depending on the time period. And if you're the one being penetrated by another man, you'll be looked down on, socially.

So with that in mind, could two men live together in a romantic relationship? Could they get married?

“A (perhaps the) fundamental purpose of formal marriage between freeborn Romans was the production of legitimate children…It is also worth considering the very term matrimonium: derived from mater (“mother”), it illustrates the extent to which the institution was identified with the creation of a mother, simultaneously suggesting that the basic function of a wife was as mother. Note, too, the complementary concept of patrimonium: derived from pater (“father”), it signifies the property that is passed down from father to son. In other words, one could say that a basic function of Roman marriage was to make a mater, pater, and liberi, the mother serving the function of creating the legitimate offspring to whom the property of the father could be handed down…In sum, matrimonium can be described as a private contract between a man and a woman (and their families) that had specific legal ramifications.” (Williams, pg 280-281)

This is from the appendix “Marriage between Males” in Craig Williams’ classic book on homosexuality in the Roman world. He presents some evidence where Roman authors talk about men being married, but it’s always in a pejorative sense, to slander someone or as a joke. For example Cicero described Mark Antony as another man’s wife, to present him as weak and effeminate, not a true Roman man. The emperors Nero and Elagabalus were also supposed to have participated in public wedding ceremonies with men, but again, this might be intended to slander them (and there are several other questions about what was going on with Elagabalus; was he transgender, maybe?) Williams also notes that poems by Martial and Juvenal mention marriages between men. They wrote satires, so these probably weren’t real marriages, but:

“neither Martial nor, for all the acerbic bombast of his language, Juvenal seems to expect his readership to react to the existence of marriages between males with a start of unfamiliarity: disapproval perhaps, but not shock.” (Williams, 280)

In other words they could have been making fun of something that was really happening and that their audience was familiar with.

There does seem to be one law from the 4th century, in the Theodosian Code, where men who “marry in the manner of a woman” can be punished with the death penalty. Is this referring to homosexual relationships in general, or does it mean (as Williams suggests) that men actually had been getting married, and that practise was now being criminalized? Of course by then, and in the later collections of Roman law from the 5th and 6th centuries, the context was much different. The empire had been Christianized and homosexual relationships of any sort were prohibited.

I suppose Williams' arguments can be debated; personally, it seems weird to me because if men were really getting married in quasi-legal ceremonies, Christian authors probably would have complained about it much more (but perhaps this is my own bias as a medievalist!).

Could women live together and marry like this? I don't think there's any direct evidence for that...generally no one has ever really cared what two women do, even in modern law! For the Romans, even if they could conceive of two men marrying, it would just make no sense, legally or culturally, for two women to get married. Women were the passive party in the marriage - the man was the one who does the act of marrying, the women is the one who has marriage done to her (there are even two different words for marriage in Latin because of this).

So, in short, gay marriage was legally meaningless, so Roman law doesn't say anything about it, except possibly for one very late law, where it is punishable by death.

Source:

Craig A. Williams, Roman Homosexuality (2nd ed., Oxford University Press, 2010)