Because this tree is practically insect and disease free, I think the finger of suspicion points to a non-living problem. Was the tree watered during the unusually dry winter? A severely stressed tree can attract borers. It is normal for the lower limbs to die off as is true for our own conifers as well. Had you made any significant changes to the yard it grows in?

For a tree, your watering schedule is likely not correct. You need to deep water to reach all the roots. Soak the area until you are sure the water reaches them. This will depend on your soil. For sandy soil 30 minutes would be fine, even extra. For loam perhaps 35-40 and for clay apply the water very slowly for an hour. Then do not water again for at least a week.

You can carefully scrape away the goo and see if there is a hole. If there is no hole, then there is probably no borer. Take a picture of the area close up once cleaned if you are not sure.