Is new schizophrenia behavior a possible sign of a brain tumor?

Yes. But, a lot of things are possible. Whether that means they are probable is a different story. I think that any changes which are drastic or come on suddenly for a person, that is something which needs medical evaluation. A condition may be reversible, but waiting may make it worse. As it's difficult to know just what you mean by schizophrenia behavior, it sounds like something requiring attention.
Schizophrenia tumor. Brain tumor, causes symptoms depending on the localization in the brain (on the cortex or deep inside). Symptoms can be atypical hallucinations, or delusions, or "fabrications" of events that do not exist while the intelligence remains relatively stable, but the sx are not constantly present. The symptoms of schizophrenia can be constant and long lasting + dulling of intellectual capacity.
Maybe. Behavioral changes can be one sign of brain tumors but generally it is not the only symptom. Schizophrenia is much more common than brain tumors.
Organic Psychosis. New psychotic episode could be new onset schizophrenia or organic factors affecting the brain such as infection, inflammation, tumors, alcohol/street drugs. Thorough evaluation & workup is warrented to rule these out.