I’m glad to hear you’ve found a solution. I’ve got a set of 8 rechargeable batteries that I swap between my 3 MX3 remotes. Interestingly, none of mine have exhibited that behaviour with CE19. But I’ve seen the default behaviour vary tremendously between versions of these remotes over the years. One would default to having the mouse pointer turn on after 30 seconds of inactivity, etc.
Anyway, glad you got it sorted.