AoA brother. Welcome to the forums.
Hmmm. Interesting problem. Bro, are these stock fitted lights? I am asking as I have not seen these lights till now in any vitz. Many users get them installed afterwards.
The reason seems to be simple. The lights are taking power from the wrong circuit. Take you ride to some good car accessories shop. The electrition over there will simply give it power through the door switch circuit. Afterwards, the lights will only glow when the door will be opened.
If you want to do it yourself then you will have to study the ELECTRONIC WIRING DIAGRAMS of vitz. This is doable but requires time. So, its better to take it to an electrition.
Best of luck,