Thanks for writing. The condition you describe is a symptom of imbalance in your body. Even a good vibrato is just a symptom of the condition of your body, as a confirmation that things are balanced. So the remedy is not to fix the vibrato. It is just telling you that things in your body are off. You need to make sure the parts of your body involved in singing are behaving appropriately.
This gets into physical functioning that is beyond what can be communicated in writing. But what I can offer is make sure you are breathing in a complete and coordinated manner. Try to stay in an inhaled position when you start to sing. Don’t allow yourself to exhale when you sing. Experiment with not moving and staying elastically stretched in your torso. Then the breath that is needed will come as a reflex.
The correct action is similar to laughing in the sense that the breath comes automatically and freely when you laugh. The difference is that when we sing it is a sustained gesture rather than a bouncing one as in laughter.
The other aspect to address is that your larynx is truly saying the vowel when you sing. It is very common for the larynx to be relaxed and inactive while singing. This will cause an imbalance in the relationship between the breath and the larynx.
These are just general points. Unfortunately I can’t be very specific to you without actually hearing your condition myself. If you would like to send a recording I could give you more accurate feedback. Thank you.