What about doing it this way.

Currently it skips any line containing the string "{T}". And if the following line consists of a single alphanumeric, that line is skipped as well.

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

my $flag_match;

LINE: while ( my $line = <DATA> ) {

    if ( $line =~ m/{T}/ ) {
        $flag_match = 1;
        next LINE;
    }
    else {
        if ( $line =~ m/^\w$/ && $flag_match ) {
            $flag_match = 0;
            next LINE;
        }
    }

    print $line;

}

__DATA__
020209990421VUTVS01 00082445B3^V^V^A2^C^D^V^V^A os00 0001 000101 R S 9
+912290449 00005941^B{T}
R
Saturday, January 1, 2000
G1
G
^C^D^V^V^A os00 0002 000101 R S 9912290451 00004113^B{T}
R
G8
Gardening<
January garden calendar
B
C
[download]

The code does more than just delete lines containing only a single uppercase letter, it also concatenates everything that remains into a single line. Is that the intent?

You actually ask how to do two contradictory things. Your first request implies deleting the line containing {T} and the following line. The last request asks that only a line containing a single letter be deleted if it follows a line containing {T}. Nowhere do you indicate if it is important that the {T} be at the end of the line.

use warnings;
use strict;

while (<DATA>) {
    no warnings "void";
    m/{T}$/ .. s/^[A-Z]\n//;
    print;
}

__DATA__
020209990421VUTVS01 00082445B3^V^V^A2^C^D^V^V^A os00 0001 000101 R S 9
+912290449 00005941^B{T}
R
Saturday, January 1, 2000
G1
G
^C^D^V^V^A os00 0002 000101 R S 9912290451 00004113^B{T}
R
G8
Gardening<
January garden calendar
B
C
[download]

Prints:

020209990421VUTVS01 00082445B3^V^V^A2^C^D^V^V^A os00 0001 000101 R S 9
+912290449 00005941^B{T}
Saturday, January 1, 2000
G1
G
^C^D^V^V^A os00 0002 000101 R S 9912290451 00004113^B{T}
G8
Gardening<
January garden calendar
B
C
[download]

Note the use of no warnings "void" to suppress the 'useless use ...' warning due to using the range operator for a side effect.

Minor alterations of the match (possibly to a substitution) can provide the other variants implied by your question.

Because you're simply reading in lines and then printing them out again, I suggest that rather than change what's in $_ you use your conditional construct (if {...} else {...}) to decide what actions to actually take with each line. Then it's a simple matter to discard another line:

if (/\{T\}/) {
    my $throwaway_line=<DATA>;
    # that line will never get printed now
}
else {
    print ; # print with no arguments prints $_
}
[download]

Basically if you just read another line from the file, and don't print it, you'll get what you want, I think. (I'm having a little trouble reading your post, so my code may not quite solve the problem you're describing, but hopefully it's close enough that you can adapt it.)

I also highly recommend using strict and warnings as standard practice.

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

while ( <DATA> ) {
    next if /{T}/ and $_ .= <DATA> and /^.\Z/m;
    print;
    }

__DATA__
020209990421VUTVS01 00082445B3^V^V^A2^C^D^V^V^A os00 0001 000101 R S 9
+912290449 00005941^B{T}
R
Saturday, January 1, 2000
G1
G
^C^D^V^V^A os00 0002 000101 R S 9912290451 00004113^B{T}
R
G8
Gardening<
January garden calendar
B
C
[download]

#!/usr/bin/perl

use strict;
no warnings;

my @lines = <DATA>;

for my $i (0 .. $#lines) {
    if ( $lines[$i] =~ /\{T\}/
      && $lines[$i + 1] =~ /^\w$/ ) {
          splice( @lines, ($i + 1 ), 1 );

    }
}

print @lines;

__DATA__
020209990421VUTVS01 00082445B3^V^V^A2^C^D^V^V^A os00 0001 000101 R S 9
+912290449 00005941^B{T}
R
Saturday, January 1, 2000
G1
G
^C^D^V^V^A os00 0002 000101 R S 9912290451 00004113^B{T}
R
G8
Gardening<
January garden calendar
B
C
[download]

open(DATA,"ss.txt") or die $!;
@data=<DATA>;
close(DATA);
foreach $i(0 .. scalar @data){
if($data[$i] =~/\{T\}/){
$data[$i]=~s/$data[$i]//g;
$data[$i+1]=~s/$data[$i+1]//g;
}
else{
print "$data[$i]";
}
}
[download]