How to wire a reactance ballast/cfl lamp???

I'm repairing a 13W cfl desk lamp (OTT-Light) that needs a new ballast. The lamp is configured with a plugin "transformer" that is the ballast. The replacement ballast (1g13CP) has just two black wires. Before I blow myself up can someone shed light on how to wire this thing? My guess is it should just be spliced into one of the wires between the outlet (120v) and the lamp. Since the wires are not marked either can be the "input" or "output" (I realise I'm probably not using the right terminology).

Thanks.

Those types of lamps don't typically use straight shot magnetic ballasts like that at mains power which is the only possible two wire device that describe a 'ballast' Can you field some more information about what you're using? Even a series magnetic ballast as you describe will have a capacitor for a striking voltage.

Modern ballasts (within the last two years) are fully electronic

Thanks. The desk lamp has a "Simple Reactance Ballast" (HB-13P-1) plug that looks like a plug-in transformer (see photo). View attachment 64914
The replacement ballast (1G13CP) has just two black wires (see photo)View attachment 64915. I don't know what a "capacitor for a striking voltage" means.

You would wire it inline with the hot wire from the wall to the bulb, does it have a starter somewhere?