Eye blinks are an interesting behavioral phenomenon that lies somewhere between the voluntary and involuntary realms. For example, we can certainly blink on purpose (e.g., sending messages in Morse ...
One-to-one is used when you talk about transfer or communications. You may use one-to-one when you can identify a source and a destination. For eg., a one-to-one email is one sent from a single person to another, i.e., no ccs or bccs. In maths, a one-to-one mapping maps one element of a set to a unique element in a target set. One-on-one is the correct adjective in your example. See Free ...
In the books from 1702, 1774, and 1860 that I link to in my examples of "one hundred and one" and "one hundred one," you will find consistent use of and (or consistent exclusion of and) in many other numbers ending in different digits.