Should I obtain permission for publishing a vector drawing based on a published photo?
What is your original motivation to create that drawing? Escape reproduction rights? Or else? 

The usual practice with museums and objects that are not involved in copyright any more because they are too old, is that you don't pay for the picture of the image if you take the picture of the image yourself. You pay if you use the image that the institution provides.

My guess is that publishing your drawing is not like 'republishing the photograph itself' because your drawing makes an original contribution that goes far beyond reproducing like for like the original photograph.

Agreed with commentators about approaching the institution out of common courtesy, if nothing else.