Why does the clock going on and off

Hello, That certainly is odd. I really do not want to speculate, and possibly cause confusion. The clock receives power at all times, and, in some models, even turning the key to the start position does not disable power. Really, a wiring schematic may be needed to find the fault, but just for good measure, find the fuse for the clock. Check that it has power on both sides, and observe for power with the key turned one click at a time, even starting. Let me know what you get back. If you aren't sure how to check for power, a test light is a great tool, and they are only a couple dollars.