The fascinus was the embodiment of the divine phallus (yourself does ask the good ones). Also, a deity, Fascinus; further, phallus effigies, amulets and spells used to invoke the deity's divine protection. Pliny called it "medicus invidiae"--a doctor or remedy for "invidia" = "envy"; "a looking upon"--associated with the evil eye (from "invidere" = "to look against"; "to look in a hostile manner"; "cast an evil eye upon". Of course, "Invidia" = "Envy"--one of the seven deadly sins in Christianity.
To the link with happiness: the protective function of the phallus was usually related to the virile and regenerative powers of an erected phallus. Though, in most cases, the emotion, shame or laughter, created by the obscenity, is the power that diverts the evil eye.
Attestation: Pliny the Elder: Natural History 28.7:
"quamquam religione tutatur et Fascinus, imperatorum quoque non solum infantium custos, qui deus inter sacra Romana a Vestalibus collitur et currus triumphantium sub his pendens defendit medicus invidiae, iubetque eosdem respicere similis medicina linguae, ut sit exorata a tergo Fortuna gloriae carnifex."
"Fascinus is the guardian not only of infants, but also of generals; in Roman religion, he is worshipped as a god, by the Vestals; as a remedy against envy, Fascinus hangs under the chariots of generals [(a phallus with wings--linking to the god, Mercury)] and protects them; and, a similar verbal remedy urges them to look back in order to conjure away Fortuna, the butcher of glory, from following behind him."
Therefore, at this moment of his own luck; success; happiness; the Roman general has to beware that the good fortune he enjoys does not turn into ill-fortune, the butcher of his own glory.
The link to the Vestals: the Vestal Virgins tended the cult of the "fascinus populi Romani", the sacred image of the phallus that was one of the tokens of the safety of the state (sacra Romana).
(Paragraphs 1,2 & 6 were inspired by the Wiki article, quoted by brianpck.)