Would excessive thirst and excessive urination caused by undiagnosed diabetes come and go for weeks at a time, or would it be pretty consistent?

That is a possibility because the insuling need varies and the pancreatic capacity may also vary as well as production of other hormones that may be interacting with insulin in the body. What is more important is to not delay but to get diagnosis as soon as possible because the variability of the glucose is what is doing damage to organs and causing long lasting debilitation.

If due to diabetes it is consistent