This is the 5796th most frequent Japanese word.
のめさ
"The Japanese word 'のめさ' does not appear to be a standard term or commonly used word. It may be a typo or a regional/colloquial variation."
The word 『飲めさ』 here is used as part of the verb 『飲む』 conjugated in a causative form.
その薬を飲めさせてください。
Please let them take this medicine.
The word 『のめさ』 is used as an interpretation for depth in thought or engagement in this sentence.
彼は新しいアイデアをのめさに考えてみた。
He tried thinking about the new idea deeply.
The term 『のめさ』 incorporates an abstract sense of profundity or thorough understanding.