Hello!
I bought a Japanese black pine bonsai about 8 months ago. I got busy and it got a bit neglected and underwatered. It's my first bonsai, so I am looking for any advice on how to revive the tree. The needles faded heavily, however, once I repotted they started turning green (or at least more than they were). I haven't had needle dropping, but the branch bark is pretty withered. Additionally, I did a quick bark test and the underbark is tan and damp. Any advice??

Re potting was not the best  thing to do to a stressed tree. This seedling looks very stressed. The wire is not good, it needs to be taken off and if you do it again then you need to do it properly. The only thing you can do with this plant is to keep it watered in a semi shaded place and hope it survives. No fertliser no pruning just water. I  suggest you buy a book and read how to look after this species, it will be many years before it is mature enough to be a bonsai.

There is no difference In how to take care for a neglected tree compared to a healthy tree.

Just avoid neglect and you will not be stressed about ill health. In order to make this tree a bonsai you need to avoid neglect at least 20 years. 8 months is nothing.