Is lunar elevation at a given location for a given day unimodal?
Yes, it is unimodal.

Earth's movement is a simple rotation, thus if the Moon were fixed on sky it will describe a circumference like the fixed stars.

From that basic movement we need to introduce Moon's own movement on the fixed stars sphere, which makes Moon not to complete the circumference in 1 day. Instead, Moon performs an arc similar to that of the fixed stars but shorter.

This circumference-like movement does not wobble, so it has just one maximun and one minimum in elevation.