Being officially the same age as you (my birthday is in August so I won't actually be 78 until then), your question is naturally of interest to me. I have no idea what my testosterone levels are but perhaps the next time I visit my doctor for a check-up I'll ask him.
All I can say is that my times improved across the board until 2008, when I set most of my best times, and since then I have improved my time for the 50 Breast, 50 free and 50 back but everything else has gone slightly backward, apart from the 200 IM , which I swam successfully for the first time last year, thus setting personal records in both long course and short course, which I am hoping to improve on this year. Hope springs eternal and I hope to improve everything else as well. I will know soon how much my hope is justified, because my first meet of the year is only a few weeks away now.
Generally speaking, it does seem that the progression has to be downwards, although there are plenty of older swimmers who are much faster than I am, so my view is that if they can do it, why shouldn't I? Did you see the reports of 91-year-old Maurine Kornfeld, who set a world record for the 800m in the World masters Championships last year in Riccione, Italy.
Here's her USMS record of swims, which I find impressive.
I have read that muscle can be built even in the ancient if they do resistance exercises. I prefer bodyweight exercises myself, although I used to do weights when I was younger. Maybe I should return to them, but I feel that for swimming technique is more important than strength. It also helps if there is someone of approximately the same standard in the same race to pull you along. Unfortunately very few over here are of my low standard.