I have never worked with non-system perl such as what perlbrew makes possible

There's no difference between a distro-installed Perl and a perlbrew-installed Perl except in which directory they are installed.

In fact, you can manage the system Perl with perlbrew simply by creating a symlink.

cd "${PERLBREW_ROOT:-$HOME/perl5/perlbrew}"
mkdir perls/system
ln -s /usr/bin perls/system/bin
[download]

It's not obvious to me that there is a cpan for each perlbrew install.

Each perlbrew has its own modules and binaries.

I cannot figure out how and where cpan will install the modules in an environment when there are multiple perls installed.

cpan asks the perl executing it for that information.

$ "${PERLBREW_ROOT:-$HOME/perl5/perlbrew}"/perls/5.20.0t/bin/perl -V:'
+inst.*'
installarchlib='/home/ikegami/usr/perlbrew/perls/5.20.0t/lib/5.20.0/x8
+6_64-linux-thread-multi';
installbin='/home/ikegami/usr/perlbrew/perls/5.20.0t/bin';
installhtml1dir='';
installhtml3dir='';
installman1dir='/home/ikegami/usr/perlbrew/perls/5.20.0t/man/man1';
installman3dir='/home/ikegami/usr/perlbrew/perls/5.20.0t/man/man3';
installprefix='/home/ikegami/usr/perlbrew/perls/5.20.0t';
installprefixexp='/home/ikegami/usr/perlbrew/perls/5.20.0t';
installprivlib='/home/ikegami/usr/perlbrew/perls/5.20.0t/lib/5.20.0';
installscript='/home/ikegami/usr/perlbrew/perls/5.20.0t/bin';
installsitearch='/home/ikegami/usr/perlbrew/perls/5.20.0t/lib/site_per
+l/5.20.0/x86_64-linux-thread-multi';
installsitebin='/home/ikegami/usr/perlbrew/perls/5.20.0t/bin';
installsitehtml1dir='';
installsitehtml3dir='';
installsitelib='/home/ikegami/usr/perlbrew/perls/5.20.0t/lib/site_perl
+/5.20.0';
installsiteman1dir='/home/ikegami/usr/perlbrew/perls/5.20.0t/man/man1'
+;
installsiteman3dir='/home/ikegami/usr/perlbrew/perls/5.20.0t/man/man3'
+;
installsitescript='/home/ikegami/usr/perlbrew/perls/5.20.0t/bin';
installstyle='lib';
installusrbinperl='undef';
installvendorarch='';
installvendorbin='';
installvendorhtml1dir='';
installvendorhtml3dir='';
installvendorlib='';
installvendorman1dir='';
installvendorman3dir='';
installvendorscript='';

$ "${PERLBREW_ROOT:-$HOME/perl5/perlbrew}"/perls/5.18.2t/bin/perl -V:'
+inst.*'
installarchlib='/home/ikegami/usr/perlbrew/perls/5.18.2t/lib/5.18.2/x8
+6_64-linux-thread-multi';
installbin='/home/ikegami/usr/perlbrew/perls/5.18.2t/bin';
installhtml1dir='';
installhtml3dir='';
installman1dir='/home/ikegami/usr/perlbrew/perls/5.18.2t/man/man1';
installman3dir='/home/ikegami/usr/perlbrew/perls/5.18.2t/man/man3';
installprefix='/home/ikegami/usr/perlbrew/perls/5.18.2t';
installprefixexp='/home/ikegami/usr/perlbrew/perls/5.18.2t';
installprivlib='/home/ikegami/usr/perlbrew/perls/5.18.2t/lib/5.18.2';
installscript='/home/ikegami/usr/perlbrew/perls/5.18.2t/bin';
installsitearch='/home/ikegami/usr/perlbrew/perls/5.18.2t/lib/site_per
+l/5.18.2/x86_64-linux-thread-multi';
installsitebin='/home/ikegami/usr/perlbrew/perls/5.18.2t/bin';
installsitehtml1dir='';
installsitehtml3dir='';
installsitelib='/home/ikegami/usr/perlbrew/perls/5.18.2t/lib/site_perl
+/5.18.2';
installsiteman1dir='/home/ikegami/usr/perlbrew/perls/5.18.2t/man/man1'
+;
installsiteman3dir='/home/ikegami/usr/perlbrew/perls/5.18.2t/man/man3'
+;
installsitescript='/home/ikegami/usr/perlbrew/perls/5.18.2t/bin';
installstyle='lib';
installusrbinperl='undef';
installvendorarch='';
installvendorbin='';
installvendorhtml1dir='';
installvendorhtml3dir='';
installvendorlib='';
installvendorman1dir='';
installvendorman3dir='';
installvendorscript='';
[download]