You can achieve that by using a lookahead or lookbehind assertions. The former will give you the start positions of the matches. The latter the ends (as you've requested).

$_ = 'TATATATATATA';
while (/(?=TATA)/g) {
    print "Matched 'TATA' at position ", pos, "\n";
};;
Matched 'TATA' at position  0
Matched 'TATA' at position  2
Matched 'TATA' at position  4
Matched 'TATA' at position  6
Matched 'TATA' at position  8

$_ = 'TATATATATATA';
while (/(?<=TATA)/g) {
    print "Matched 'TATA' at position ", pos, "\n";
}
Matched 'TATA' at position  4
Matched 'TATA' at position  6
Matched 'TATA' at position  8
Matched 'TATA' at position  10
Matched 'TATA' at position  12
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while (/TATA/g) {
    print "Matched 'TATA' at position ", pos, "\n";
    pos() -= 2;
}
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and

while (/TA(?=TA)/g) {
    print "Matched 'TATA' at position ", pos, "\n";
}
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(?=TA) is a zero-width positive look-ahead assertion and is documented in perlre

Both these techniques also match at 2 which might not be what you're after

So, obviously, the /g leaves me positioned at the end of each successive match. But, if I wanted to also match at positions 6 and 10, would I need to respecify pos to be the beginning of the previous match +1 character? Is there a better, more straightforward way to do this? Am I just missing something simple?

Judging from code like GrandFather's at finding number of contiguous letters, there may be other and somewhat more terse ways. But personally I'd do it like you suggested, and that would be clearer for me to understand. Of course It will be enough to step back by -2 on the current pos.

Fortunately IIRC Perl 6 will provide simple single modifiers to do this kind of things out of the box. (In spite of those who claim it's "too much complexity". ;-)

Since I didn't see anyone mention this (now watch someone submits a node that does while I'm busy typing), if you don't really need a regular expression, you might be better off just using index

#!/usr/bin/perl

$_ = 'TATATATATATA';
$str = "TATA";
$p = -1;
while (1) {
    $p = index($_,$str,$p+1);
    last if $p < 0;
    print "Found $str at position $p\n";
}
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