I have two node apps running on my server, each performing different tasks.
However, I now need to create a service that is going to be used by both of them. Obviously I don't want to create it in both of the apps, hence creating two codes to maintain.
My current thought is to have a separate repository only for this service, then require it from each app as an outsourced module.
I was wondering whether there are better methods, or if this method might encounter problems I'm not seeing
Well if you strictly follow the rule that shared means only shared things in the common package, I don't see any issues with that. The problem comes when you try to put the logic in one repo which is supposed to be only used for one. In that scenario you will need to rebuilt both apps as the repo or package is depedency of both.
One issue that I have seen people face is when they work with shared repo is that when you need to tweak things just because they are at common place. for example you have a method that does one job and suddenly you want to use that in other place as well but with a tweak. In that case you end up modifying the shared code to support the second repo but since it is shared, you will have to do regression testing of both apps.
I see shared repo candidates being drivers, client etc. I guess rest is up to your project structure and judgement. In this case there is nothing correct or incorrect. Hope this is making sense.