Have you tried turning the ballast the other way around, so it is in the other mains lead? In general with PL9 lamps, avoid the Chinese made ones like the plague, because, to a lamp, they are all utter garbage. Try to find one made in EU, probably Poland, as they still make lamps there, or an older GE made in the USA. those ones made in the EU or USA work well, and last a long time. The ballast if it is a magnetic one rarely fails, it will fail short circuit and blow the lamp.
Otherwise you can get a small metal industrial case, a power switch and a pair of cable glands, and a 9W iron core ballast, and replace the existing one, but the plug in type is pretty much not going to be available.