So this issue is not exclusive to the CBX but also impacts many other models and makes not just Kehein. I have analysed the issue in detail. The issue is two-fold, in a limited number of cases the overflow tubes corrode due to galvanic reaction caused by ethanol oxidising into acetic acid and the decay process exacerbated by the acid and galvanic reaction. The second and more common issue is the tube micro fracturing due to the residual stresses from the cold rolling process during tube manufacture. The tube is pressed into the bowl using an interference fit which reduces the pressed in diameter by approximately 0.05mm or two "thou". This causes further stress and over the years micro-fractures permeate up and down the base. In some cases, these fractures are so small even with an eyeglass they cannot be seen. Soldering, JB weld etc will not work long term whatever anyone tells you I have seen the many failed attempts in this regard (and tried them all myself). The crack will permeate through to the pressed in part of the tube where the solder will not adhere and it will leak. Ethanol dissolves the polymers in epoxy-based adhesives and shortly again it will fail.
To test firstly make sure the drain screw is tight and the overflow passage is clear using a 1.9mm drill bit. Fill the bowl with water, using compressed air at NO more than 40 PSI put your finger over the top of the tube and gently release air into the overflow outlet at the base, you will soon see bubbles coming to the surface if it is fractured. The replacement tube has been supplied with a soft lead seal to avoid the stresses previously mentioned and should never fail in the future.
You can either send the bowl for repair to us at The Super Sport Shed or alternatively fit them yourself, this is a relatively simple process but requires a sturdy drill press to undertake the job (the small cheap ones are unlikely to be man enough).
You can buy the individual part here:- https://thesupersportshed.com/staging/product/carburettor-bowl-overflow-tube-qty6/
Tighten the old overflow tube in the drill chuck and gently twist back and forth, either the tube will release or snap at the base, if it comes out great, don't worry if it snaps off. If it snaps use a 3mm (second preferred) tap in a pin vice (or similar) and tap down through, the broken bit will release keep twisting in the same direction and pull it out, this has never failed me yet and I have done many dozens to date. Use a pair of pliers to remove the remaining tube from the tap.
To insert the new tube put the replacement overflow tube in the drill chuck, tighten it firmly but not overtight which will crush the tube! Pack the bowl underneath to ensure its level and press the tube in a "one-shot" action, if you stop it will be very difficult to press it in further so I recommend removing it (by twisting back and forth) and trying again. If you overshoot a little don't panic, again very lightly twist back and forth and pull down gently to get to the desired height (level with the top of the float bowl), you will have a limited opportunity to get this right otherwise it is likely to leak if you miss more than once. It has never failed me yet!