I've had a few mad-mads lose tails, or sections of tails. These were the result of things like unexpected gecko movements and me closing the end of the tail in the door, and impulsive gecko running out of tank + very alert and fast cat. The squirming dropped tail is gross IMHO but works well -- the cat focused on that and the gecko got away!
I have never used antiseptic on the wound at all, since my info is to only spray water on it if anything, and that they have a strong immune response themselves.
The tails grow back slowly, especially if it's a big piece. They look like they kinda telescope out, so it's an interesting process! They start out brownish, which is unfortunately about the color of a nice roach or flying termite, so has been bitten off by the mate -- a point for keeping them singly like you're doing!! Eventually the tail turns green and looks much like the rest of the gecko, though scalation is often a little different, and there is a line where the new meets the old. The tail winds up a little shorter too. So you can tell it's a regrown tail, but it looks OK. They might need extra food while regrowing a tail, since this is a pretty big body part that the gecko uses for storing their body's reserves.
Best of luck to you and the gecko! Did you ever determine why her tail was so funky in the first place?