Diseased Bird: Injury/deformity/tumor of male house finch

This male house finch has been at our feeders for 3 weeks with possible worsening of his condition. He seems to be able to eat only from a platform feeder (sunflower chips) and drinks from a bird bath. Recently he is shaking his head. In most years, we have seen several finches with Mycoplasma eye disease, but are not seeing any this year so that seems unrelated. Thank you for any insight you can give.