Thanks for the question.

My initial observation was that the "sap" appears to be at the pruning marks of smaller branches, however, that does not explain the bottom of the tree.

I send this to the plant pathologist and he said that if it were just transpiration stress from pruning scars, gummosis would be an option.

But, he suggested you check for borers. There are several that like pomegranates, but one is very small. Look for exit holes and that will be a confirmation. The link below will show an example of what to look for. Keep in mind, you'll have to look carefully if the borers are super tiny. https://extension.missouri.edu/publications/g7190