Being actually a hallucination of pananoid teacher Peredonov, this character embodies such qualities as platitude, drab, anxiety, lack of life. The element "недо-" suggest the lack of something, while - тыкомка would mean something like a nasty small creature that lurks everywhere (тыкаться), or can be associated with slang "head" (тыковка).

Anyway, it is a fictional word coined by Sologub and it doesn't have any specific meaning in Russian.