Normally I would say put some raw honey on it, but if they lick it off, it could cause issues.
I’m not very versed in gekos, maybe @t_h_wyman could answer your question? I think a vet visit would be an idea since it’s close to the cloaca, even if this particular species of geko can shed it’s tail and regrow.
Aaawwwww. Poor little guy! Maybe you could apply some vitamin E oil on it? But if there is swelling there might be an infection going on which would definitely warrant a trip to the vet……
If the tail was usable when you got him but now isn’t, I’d take it to the vet. Had something similar happen with a cat. The tail wasn’t broken, she had an abscess, but due to the lack of space in the tail itself, an infection can put pressure on the spinal nerves. This causes a loss of sensation and tail function. The longer it’s left, the more likely the damage will be permanent.
First, the swelling is a bit of a concern and could indicate an infection. As a start I would use a topical on it like Neosporin (WITHOUT numbing agent as that has proven toxic to a number of herps) but I would also advocate a visit to a vet.
Second, “floppy tail” is something that was not uncommon with grandis a while ago. It was usually an indicator of an improper diet, back in the days before things like Pangea/Repashy/etc. It can also be a side effect of injury as well as an indicator of stress from overcrowding or being stuck with an overly dominant animal. Once it has happened it is unlikely the animal’s tail will ever return to normal behaviour