IANA holds 9081/tcp Reserved, so in practice it is the port the second app server got.
The registry marks 9081/tcp Reserved and assigns 9081/udp to cisco-aqos. With no TCP assignment, what you find is a local choice — most often the next HTTP port after 9080 when two Java application-server instances share a host, or a sidecar or metrics endpoint of whatever runs on 9080. Its meaning is entirely inherited from its neighbour, so look at 9080 on the same host first.
Expose with care
Same treatment as the 9080 service it usually accompanies: plain HTTP behind a proxy, never published raw.
$ curl -sI http://TARGET:9081/Seen this on your network? Beige Box scans your Wi-Fi and shows every open port on every device — and its Ports tool links straight back here.
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Corrections or a missing port? Reply @rimrocksystems.