Symbolism, Imagery, Allegory
There are a couple of references to being "on the wagon" in the play, and they definitely seem to be part of a larger metaphor for quitting bad habits generally—you know, like incest.
May mentions early on that she's "on the wagon" in the classic sense—that is, that she's taking a break from alcohol (150). However, that changes in the blink of an eye once she and Eddie really start arguing, and he storms out for the second time in his visit. After a good solid cry fest, when she hears Eddie returning, she apparently wants to look busy, so she goes and takes a swig from the bottle of liquor on the table and stares at it as he reenters.
Eddie, too, claims that he's mostly been on the straight and narrow lately—in terms of alcohol and everything else:
"Well, I haven't dropped the reins in quite a while ya' know. I've been real good. I have. No hooch. No slammer. No women. No nothin'. I been a pretty boring kind of guy actually." (225)
Who knows how true that is? But in any case, like May, Eddie's return to alcohol coincides with their reunion.
Of course, the real "drug" in the play seems to be May and Eddie's insane feelings for each other, and Shepard seems to use the frequent references to alcohol/quitting alcohol to underline that other incestuous little addiction. May and Eddie might have been on the wagon from alcohol and each other up to that night, but they are indulging fully and freely in both addictions by the time the play is over.