Bizarre Behaviour with CFL Ballast (light turns on when I touch the physical ballast)
This is extremely common behavior for old fluorescent ballasts, though the reason for it depends on exactly what type of ballast it is.

If it is a really old model that uses a replaceable "starter" cartridge, it is likely that the starter needs to be replaced.

If your ballast does not require a starter, the issue most likely the lack of a ground plate behind the bulbs. "Rapid Start" magnetic ballasts require the metal plate that makes up the back of the fixture to be grounded, which provides a pathway for the "radiated" high voltage current that starts the lamp.

If the fixture is already properly grounded and this is still an issue, then it is likely that the ballast is failing and is just too weak to provide a good starting current.