Is that all sticking to a magnet or is it just floating in the ATF?
i would say its high mileage, high wear, and varnish
If that is the Original trans fluid, its possibly animal byproducts and separating addittives etc...
If its an old fluid, but after 1975 before 1990s or early 90s, its not so much animal byproducts likely, but it could be just be a cumulation of clutch mud, debris the filter couldnt take, varnish, any additives someone may have added, etc...
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this is dexron 2 on the left when its not old and worn(looks dark) and on the right(worn and burnt, trans is toast)
your fluid being deep red is interesting.
I dont want to recommend anything that could hurt it, but without knowing its history, and the red is still red.
I would strain some of your old fluid, like a couple quarts, let some sit to see if it has separation of anything happen, if it doesnt, Use that and a very conservative change of DEXIII spec fluid from walmart or something.... new filter... drive.
I would also do a shift kit, but before driving.
I would change that fluid after some amount of miles. Also check your trans cooler for plugging and flow, clean it if it needs some attention(its in the rad)
The reason for the conservative change is new ATF has cleaners, your system might have untold **** just waiting to dislodge and plug a cooler line.
But you may have a not-old unit that could go for a adjustment or a shift kit... hard to say