Thank you, trents and knitty kitty!  You have confirmed what I thought:  Clean living from a gluten-free perspective has meant basic tests would show low-to-no antibodies. It was my doctor who was wondering if I even had it, based on these tests.  He's not a gastro-doc, but otherwise a kind and competent doctor. He seems genuinely interested in what it means to be celiac, and also seems only somewhat familiar with tests & protocols. Hey, at least he's open to learn. Me, I never had a doubt.  I just wondered if these tests indicate that I'm doing a good job and the answer is Yes.  Hooray! As for the concern over my high overall IgA, I recently injured myself helping a friend not die, and I have loads of inflammation in my lower back and hips at the moment.  Perhaps that is the source of the high IgA? Dunno.  I dragged a short 200 lb woman around her kitchen like a sack of potatoes as I repeatedly did the Heimlich maneuver (I am quite tall, so kinda had to pick her up). Successful after the 8th heave-ho, to our mutual relief. Good ol' Navy medical training came in good for something!  But later, after the adrenaline wore off, I was in paaaaain. I wonder if another source was that I recently had a bad cold, like to the point of taking a COVID test (neg), which knocked me on my butt for a couple weeks. The tests came just a couple days after I was symptom-free. Could that do it? My big takeaway:  I have done well in avoiding gluten.  So huzzah for that. Thank you both.

@Kipman, Ask for a genetic test to determine if you have any of the known genes for Celiac Disease.   Anemia, Thiamine deficiency and diabetes can each cause false negatives and low IgA.  You may want to investigate these further with your doctor. Celiac Disease can occur with Ehlers-Danlos Syndrome, another genetic autoimmune disease.  Ehlers-Danlos is a connective tissue disease frequently seen in people who are double jointed or have stretchy skin.  This stretchy-ness can affect the digestive system.   https://pubmed.ncbi.nlm.nih.gov/27321543/

Welcome to the forum, @Travel Celiac! You have to be consuming gluten for your body to trigger the autoimmune response and produce anti-gluten antibodies.  If you're not consuming gluten, the autoimmune response is not triggered and you won't produce anti-gluten antibodies.  Celiac Disease is genetic.  Your genes don't change.  You will always have the Celiac genes whether you eat gluten or not.   Your negative tTg-IgA  shows that you are successfully keeping gluten out of your diet.  You are doing very well on that point, but you still are Celiac.  Be proud of your accomplishment!  

I've never heard it said that celiac disease is a connective tissue disease. It is an autoimmune disorder that (classically) attacks the lining of the small bowel but we now know it can manifest in other body systems. It is also true that autoimmune disorders tend to cluster. That is, when you have one you often develop others.

I did for a week, though that was 4 weeks before I had the test done. The doctor told me the lab rang her and said they hadn't seen results like it in their lab. Them being nearly all indeterminate that is. I also tested positive for a multiple connective tissue disease but when they did further testing it was all indeterminate too (I've only just realised that celuac is a connective tissue disease)