go install does not add the binary under GOBIN when running as cloudinit userdata script

I am trying to install this package: github.com/czerwonk/bird_exporter
After installing golang like so:

    GO_VERSION=1.17.1
    curl -L https://golang.org/dl/go${GO_VERSION}.linux-amd64.tar.gz -o go${GO_VERSION}.linux-amd64.tar.gz
    tar -C /usr/local -xzf go1.17.1.linux-amd64.tar.gz
    mkdir /root/go
    export GOPATH=/root/go
    export PATH=${PATH}:/usr/local/go/bin:${GOPATH}/bin
    echo "export GOPATH=${GOPATH}" >> /root/.bashrc
    echo "export PATH=${PATH}:/usr/local/go/bin:${GOPATH}/bin" >> /root/.bashrc

I install the package like so:

    BIRD_EXPORTER_VERSION=1.2.6
    go install github.com/czerwonk/bird_exporter@${BIRD_EXPORTER_VERSION}

When running all these commands on the EC2 instance manually, I end up with the package under the default GOBIN location:

    file /root/go/bin/bird_exporter 
    /root/go/bin/bird_exporter: ELF 64-bit LSB executable, x86-64, version 1 (SYSV), dynamically linked (uses shared libs), not stripped

When the same commands get executed by cloudinit in the userdata script, the packages get installed fine under /root/go/pkg/ but there is nothing under /root/go/bin/.
The logs show the downloading of all packages fine:

go: downloading github.com/czerwonk/bird_exporter v0.0.0-20210702094413-c9985a3895a4
go: downloading github.com/prometheus/client_golang v1.11.0
go: downloading github.com/sirupsen/logrus v1.6.0
go: downloading github.com/czerwonk/bird_socket v0.0.0-20190111125930-6c39d61f8853
go: downloading github.com/prometheus/client_model v0.2.0
go: downloading github.com/prometheus/common v0.29.0
go: downloading github.com/beorn7/perks v1.0.1
go: downloading github.com/cespare/xxhash/v2 v2.1.1
go: downloading github.com/golang/protobuf v1.4.3
go: downloading github.com/prometheus/procfs v0.6.0
go: downloading golang.org/x/sys v0.0.0-20210603081109-ebe580a85c40
go: downloading github.com/matttproud/golang_protobuf_extensions v1.0.1
go: downloading google.golang.org/protobuf v1.26.0-rc.1

I would like to understand what the difference is for go install in these 2 scenarios so that I can have proper control over installing the package

P.S. go get, which is deprecated, has the same result.

This issue has been resolved.
The reason for the confusion was the log output as it was hard to read, but eventually I found this:

build cache is required, but could not be located: GOCACHE is not defined and neither $XDG_CACHE_HOME nor $HOME are defined

HOME is not set when cloudinit runs. Golang apparently requires it to determine GOCACHE. I would expect this to be under GOPATH.

The solution is to also export GOCACHE:

export GOCACHE=/root/go/cache