The exact answer depends on the drop you are switching from as well as your own body chemistry. Your genetics can determine how quickly you clear drugs from your system. However, I can give you a rule of thumb.
At a minimum, I would give it two weeks. In most cases, the prior medications will have from zero to negligible effects two weeks after being discontinued.
Therefore, the several days of home intraocular pressure monitoring toward the end of those that period can be assumed to be free of any influence from the prior medication(s).
However, if you want to be even more confident, you could give it four weeks. By four weeks you can be almost absolutely certain that all the prior medication is out of your system or at least no longer producing any effect on your IOP.
My personal experience is that timolol, normally a very short-lived glaucoma medication, continues to exert strong effects on my IOP for more than a week after a single drop. Therefore, I would certainly have to allow two weeks washout before I can be confident my IOP is no longer reduced because of that medication.
Various published studies use different washout periods, but four weeks is a common one. I seem to recall reading some studies with two week washout periods. That duration seems reasonable for home monnitoring, but for a clinical study I think it is too short.