I am so sorry to get to your post so late. I have never heard of this being a typical Down syndrome characteristic or trait. I think that just as tics are part of the general population, we have to remember that people who have Ds are affected by the same other illnesses, heath issues, mental health issues etc. I don't think that we always remember to assume that when things happen to anyone with Ds that it is, as is for the general population. Now having said that, there are some things that are specific to Ds like delays or hypotonia, but realistically, with other irregular or regular happenings (just as the human brain or body endures or discovers things) - those same things can or do happen to you or I.
What I would suggest to you in order to help your sister, is do the same thing as if it were your mother. If your mother or friend had a late onset of tics, what would you recommend they do? I would consult with them and suggest that they have their doctor rule out any medical reason for these tics to occur. Is the jaw popping, teeth grinding, head shaking, clearing her throat have something to do with something medical? When I read those specific tics, it leads me to wonder if she is reacting to an ear infection. I know when my ears are plugged, those are some of the actions I do, subconsciously to try to get my ears to pop or unplug. You mentioned that she had never done these specific tics before, (and I realize you mentioned that she does mimic behaviours she discovers) but in this case you might want to rule out any medical reasons that might have encouraged the actions in the beginning, which may have now become somewhat semi-permanent tics. The problem with doing this though is if she did have an ear infection at one time, (for instance when you first noticed her doing these actions) that same ear infection might be long gone, and the behaviours are now just repetitive actions. In a way, it's almost too bad no one examined her ears when it first started, because I think even though she mimics, I think those are pretty specific tics that would be hard to discover all at the same time and then just out of discovery, repeat them all the time to a point where she knows it bothers you and has said she can't help it. I know you are concerned, and also that it upsets you that it's bothering you especially if she can't help it, but dig deeper. I do believe there has to be a logical reason for her doing it (even if that same reason no longer applies). I am just wondering, who in your family is her primary care giver? Or is she living independently? The reason I ask is, perhaps you can encourage whoever has taken responsibility to ensure her medical needs are met, to take her to her doctor and see why the tics are still occurring.
I applaud you for being such a caring sister.
In addition to anything I have mentioned, please keep in mind, that while I or others may have extensive knowledge in many areas, you should always seek professional medical advice from your own physician, as it pertains to medical conditions or concerns.
Good luck, and if you have any other questions that I can help you with, please feel free to message me directly.
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Children - Special Needs Community Leader;
Down syndrome Community Leader & Ds Group Forum Founder/Moderator