i know when i had pinkeye i went to bed fine and then woke up the next day with my eye crusted shut but that occurred overnight not like a BOOM sudden thing
It's a binary switch, it can fire not as fast but they either fire or they don't so if a nerve is not working it's often gonna be like flipping a switch
Most any nefarious effects aren't going to show immediately, if they want to populate the planet they can't just kill, sterilize, or cause severe effects in the fist batch of people before the first several batches have had an infection
They'll also need the effects to be far out enough from the vaccine where they can feign probable deniability and say "woah hold on let's not jump to conclusions like crazy conspiracists"
And even if it is at that point once the initial outrage dies down among the panic people will be more willing to swallow, "the emergency of the times demanded it, it's unfortunate we had this unforseen outcome"
