Hello and welcome. My name is ***** ***** I'm a biologist with a special interest in reptile health. I'm sorry to hear of this problem.
I know you would like a home remedy, and I would love to give you one, but I believe you deserve honesty. When the tail is infected, a condition called dry gangrene is common. Sometimes it's the result of a minor injury (possibly caused by the other gecko, but sometimes no original cause can be found. Because the infection can keep spreading up the tail, and into the spine, it's best to have it treated by a vet. It can be fatal if allowed to continue. This site will let you enter your zip code to find the nearest reptile vet:
You can read more about tail infections on this page:
The information applies to other species, as well as iguanas.
The vet may have to amputate the infected part of the tail. In geckos, it does often grow back.
I would also permanently separate the two geckos. Two males simply cannot be kept together. Severe fighting, leading to serious injuries is common.
If you have more questions, let me know in a REPLY. I hope your gecko will reach a full recovery.
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