Dimensionless axis plots How to properly label graphs that can be dimensionless?

One of reviewers of my document strongly emphasised on labelling plots with which I generally strongly agree. On this occasion, however, I was explaining a general mathematical model on generated time series and by time series I mean an observation (value of a variable) that changes. Non of the variables I'm plotting has any units and the only reason why I added label Time [s] on x axis so that reader doesn't have to think too much what is there. Reviewer suggested adding units to all other labels, such as dimensionless amplitude, amplitude square and inverse of amplitude square. It seems that adding Density [1/|1|^2] or making up a unit might be considered a bit offensive.

Here are examples, where I am supposed to label axes. None of used variables requires a unit.

Density of dimensionless variable.

Time series
Lack of a unit never implies that a clear label isn't necessary.  How can time not have an appropriate, non misleading label?  How about "Index" or "sample number"?  Just because it doesn't have a unit doesn't mean that you can't come up with an appropriate label?  Even "Normalized Amplitude" or something.  If the lack of a  unit isn't immediately apparent, sometimes "unitless" where you would normally include a unit will clear things up.

Lastly, look toward your literature.  If you can't find an example close to what you're doing, you may be reading the wrong literature, or not reading enough of the right literature.  Having to ask about something like this is somewhat of a red flag on your due diligence.