I believe I need to make a hash of team containing an array of (unique)location containing an array of tools and their number. Or maybe a hash of hashes of hashes? I've been trying just about every permutation I can think of for days.

Pass your required output to an XML parser that uses data structures and see what it produces; and then mimic it:

#! perl -slw
use strict;
use Data::Dump qw[ pp ];
use XML::Simple;

my $xml = XMLin( \*DATA, KeepRoot => 1, NoAttr => 1 );
pp $xml;
print XMLout( $xml, KeepRoot => 1, NoAttr => 1 );

__DATA__
<ToolLocations>
  <ToolLocation>
    <LocationName>location_4</LocationName>
    <ToolList>
      <Tool>
        <ToolName>tool_2</ToolName>
        <ToolNum>5</ToolNum>
      </Tool>
      <Tool>
        <ToolName>tool_5</ToolName>
        <ToolNum>3</ToolNum>
      </Tool>
    </ToolList>
  </ToolLocation>
</ToolLocations>
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Produces:

C:\test>1001808
{
  ToolLocations => {
    ToolLocation => {
      LocationName => "location_4",
      ToolList     => {
                        Tool => [
                          { ToolName => "tool_2", ToolNum => 5 },
                          { ToolName => "tool_5", ToolNum => 3 },
                        ],
                      },
    },
  },
}

<ToolLocations>
  <ToolLocation>
    <LocationName>location_4</LocationName>
    <ToolList>
      <Tool>
        <ToolName>tool_2</ToolName>
        <ToolNum>5</ToolNum>
      </Tool>
      <Tool>
        <ToolName>tool_5</ToolName>
        <ToolNum>3</ToolNum>
      </Tool>
    </ToolList>
  </ToolLocation>
</ToolLocations>
[download]

That takes your required output as input, converts it to a data structure and then converts it back successfully. So now you know what the data structure needs to look like.

So use CPAN libraries such as Text::CSV to read your CSV data instead of simply reading it line by line and using split

(my $team, my $loc, my $tool, my $amt) = (split /[,]/)[1,2,3,4];
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my ($team, $loc, $tool, $amt) = (split /[,]/)[0,1,2,3];
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my ($team, $loc, $tool, $amt) = split /[,]/;
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The index of the first element of an array/list is 0, not 1!

Could be done via both Hash of Hashes as well as Hash of Arrays

See if this works....

Input File

team_1, location_2, tool_1, 4
team_3, location_1, tool_3, 3
team_2, location_3, tool_3, 2
team_2, location_4, tool_2, 5
team_3, location_2, tool_5, 3
team_1, location_1, tool_3, 1
team_2, location_4, tool_5, 6
team_4, location_2, tool_5, 3
team_5, location_4, tool_4, 2
team_2, location_4, tool_5, 3
team_3, location_3, tool_4, 4
team_2, location_4, tool_5, 3
team_4, location_1, tool_1, 1
team_1, location_3, tool_5, 3
team_3, location_2, tool_5, 5
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Code

use v5.14;
use Data::Dumper;
my %locHash;

foreach(`cat dataFile`){
    my ($locName, $toolName, $toolNum)=(split(/\,/,))[1..3];
    $locHash{$locName}->{$toolName}=$toolNum;
}

print "Data::Dumper:\n";
print Dumper(\%locHash);

say "<ToolLocations>";
foreach my $locName(sort keys %locHash){
    say "   <ToolLocation>";
    say "       <LocationName>",chomp($locName),"</LocationName>";
    say "       <ToolList>";
    foreach my $toolDetail(sort keys %{$locHash{$locName}}){
        say "       <Tool>";
        say "           <ToolName>",chomp($toolDetail),"</ToolName>";
        say "           <ToolNum>",chomp($locHash{$locName}->{$toolDet
+ail}),"</ToolNum>";
        say "       </Tool";
    }
    say "       </ToolList>";
    say "   </ToolLocation>";
}
say "</ToolLocations>";
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Output

Data::Dumper:
$VAR1 = {
          ' location_1' => {
                             ' tool_3' => ' 1
',
                             ' tool_1' => ' 1
'
                           },
          ' location_3' => {
                             ' tool_5' => ' 3
',
                             ' tool_3' => ' 2
',
                             ' tool_4' => ' 4
'
                           },
          ' location_4' => {
                             ' tool_5' => ' 3
',
                             ' tool_2' => ' 5
',
                             ' tool_4' => ' 2
'
                           },
          ' location_2' => {
                             ' tool_5' => ' 5
',
                             ' tool_1' => ' 4
'
                           }
        };
<ToolLocations>
   <ToolLocation>
       <LocationName>0</LocationName>
       <ToolList>
       <Tool>
           <ToolName>0</ToolName>
           <ToolNum>1</ToolNum>
       </Tool
       <Tool>
           <ToolName>0</ToolName>
           <ToolNum>1</ToolNum>
       </Tool
       </ToolList>
   </ToolLocation>
   <ToolLocation>
       <LocationName>0</LocationName>
       <ToolList>
       <Tool>
           <ToolName>0</ToolName>
           <ToolNum>1</ToolNum>
       </Tool
       <Tool>
           <ToolName>0</ToolName>
           <ToolNum>1</ToolNum>
       </Tool
       </ToolList>
   </ToolLocation>
   <ToolLocation>
       <LocationName>0</LocationName>
       <ToolList>
       <Tool>
           <ToolName>0</ToolName>
           <ToolNum>1</ToolNum>
       </Tool
       <Tool>
           <ToolName>0</ToolName>
           <ToolNum>1</ToolNum>
       </Tool
       <Tool>
           <ToolName>0</ToolName>
           <ToolNum>1</ToolNum>
       </Tool
       </ToolList>
   </ToolLocation>
   <ToolLocation>
       <LocationName>0</LocationName>
       <ToolList>
       <Tool>
           <ToolName>0</ToolName>
           <ToolNum>1</ToolNum>
       </Tool
       <Tool>
           <ToolName>0</ToolName>
           <ToolNum>1</ToolNum>
       </Tool
       <Tool>
           <ToolName>0</ToolName>
           <ToolNum>1</ToolNum>
       </Tool
       </ToolList>
   </ToolLocation>
</ToolLocations>
[download]

It might help to consider that the notion of references can really be your best-friend.   Feel Free™ to have any number of references to the same bit of data.   If you need to very-quickly locate pieces of data based on multiple, non-unique, key values, you could (for example) easily create a hashref which points to an arrayref containing references to the same bits of data ... which, in the end, only occur in-memory once.