My first Basenji would have nice bright white eyes. I would take her mnt biking with me and her eyes would be red and watery. My other 2 never experienced this.
It's probably allergies. The older I get, the worse my allergies get. I have also developed new allergies. Things like Russian Olive never bothered me, now my eyes start flowing and my sinuses become highly irratated. If the concentration is high, I have trouble breathing.
Talk your vet about OTC allergy medications and dosage.
If your Basenji shows the same symptoms indoors and they do not improve, consider having your ducts cleaned and an electronic air cleaner installed.