I have a single 8-bit byte ...

$item = 0x37;  # ...or 00110111b
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If I had to guess about what's ruining your day when you try to use vec() (and I do because you haven't shown us your code) I'd say you are getting confused by the way Perl handles numbers. Perl isn't C and $item = 0x37; is not a single byte like char item = 0x37; would be in C. It's two bytes: "55". To get a single byte use chr() or a string containing a single byte (like "\x37") instead.

$ perl -le 'print vec(0x37, $_, 1) for 0..7'        # Ooops!!!
$ perl -le 'print vec(chr(\x37), $_, 1) for 0..7'   # Much better. 
$ perl -le 'print vec("\x37", $_, 1) for 0..7'      # This works too.
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Using unpack you have to jump through a few more hoops to get the same thing. You can unpack with a template of "b*" (or "B*" for reverse bit order) but that then gives you a string of 1s and 0s. You can unpack that with "c*" to get one value per bit... but the values won't be what you expect. Instead of "0"s and "1"s, you'll get "48"s and "49"s (i.e. ord("0") and ord("1").) So, to get the actual "0"s and "1"s you want, you have to then use chr(). Putting it all together gives something like this:

   
$ perl -le 'print for map chr, unpack "c*", unpack "b*", chr(0x37)'
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-sauoq
"My two cents aren't worth a dime.";