This works:

use strict;
use warnings;
sub test_a;
sub test_a { my $arg = shift; ref($arg) ? test_a$$arg[0] : $arg }
sub test_b { my $arg = shift; ref($arg) ? test_a$$arg[0] : $arg }
print test_b[42]; # prints '42'
print test_a[42]; # prints '42'
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The reason your original one fails is that while perl is parsing the body of sub test_a, it encounters test_a$$arg[0] and isn't quite sure how to parse it. You'd want to parse it like:

test_a($$arg[0])
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But it actually gets parsed like this:

${ $arg }->test_a([0])
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That is, it assumes you're calling the test_a method on $$arg via the indirect method syntax.

It makes this assumption because while the body of test_a is being parsed, there is no function called test_a in the symbol table. So it assumes that you cannot really mean test_a($$arg[0]).

Pre-declaring sub test_a; (as per my example) solves this. The other solution is to avoid the ambiguity in your syntax and add parentheses.