Here is an SSCCE showing that it works fine for me.

#!/usr/bin/env perl
use strict;
use warnings;

my $debug = 1;
my @input = <DATA>;

read_gage_header (\@input);

sub read_gage_header {

  my ($data, $header, @headers, $ettb_no, $year);
    
  $data = shift;
  
  #Now get ettb_no
  $header = $data->[0];
  @headers = split / /, $header;

  #NOTE: this print yields expected results
  print "HEADERS before ettb_no @headers\n" if defined ($debug); 
 
  #NOTE: this gets the proper ettb_no
  $ettb_no = $headers[4];                                        

  #Skip to get to Year
  shift @$data; 
  shift @$data;
  shift @$data;  
 
  $header = shift @$data;
  #NOTE: this gives me "Year 201"
  print "HEADER before year $header\n" if defined ($debug);       

}

__DATA__
 Gage Information - 240CN - 240 FEEDER CANAL                        
  SUPPLY TO 240 FEEDER FROM BELEN HIGH LINE CANAL                     
+                          
                                        
  Year 2019

  Month  Day  Time   Height   Discharge
             (mst)   (HP ft)   (QR cfs)
  -----  ---  ----   ------   ---------
  July    29  1230    5.54        80

  ... more data ...
[download]

Which produces this output when run:

$ perl 11109714.pl 
HEADERS before ettb_no  Gage Information - 240CN - 240 FEEDER CANAL   
+                     

HEADER before year   Year 2019
[download]

In other words, the problem is with the code that you haven't shown us - the part where you read in the input and populate your $data.