The coil of the relay will connect to the 120V connection on the ballast, and the common (neutral) connection.
The quartz lamp will connect to the switched leg of the relay, and the neutral connection.
The quartz lamp is 120V,not 347V. The 120V tap on the ballast will provide the 120 that the lamp requires.
**Keep in mind that some of the newer restrike methods are current sensitive, and will have different connections. That's why I said generally in my post above**
