Can you test Rogaine in only a small part of your head before committing to use?

Topical Rogaine works best for androgenetic alopecia.  If you wanted to test a small area for this diagnosis you certainly can but you need to give it a few months to see the results.  I am not sure you will see the desired results if you are using it to treat chronic telogen effluvium, but you can certainly try.  The best treatment is to remove the trigger/stressor.

No, if you have CTE you can't use Rogaine in a small area to evaluate shedding patterns. You won't be able to keep tract of changes in shedding. However, if you have androgenetic alopecia or some other form of hair loss, then yes you can use Rogaine in the test area.

Yes, you can test minoxidil (Rogaine) in a small patch of your scalp to see the value of it. It will take months to find out