We're all unique in our own way
5. Retina 0.8.2 -m, 8 available bytes
The code is given as three separate files. Here are their hexdumps:
00000000: 002a 0f2a 062a 092a 042a 142a            .*.*.*.*.*.*
00000000: 4545 4545 4545                           EEEEEE
00000000: 45                                       E

This outputs 6. Try it online!
The first file uses bytes 0, 15, 6, 9, 4, 20, and 42, and the other two files consist entirely of E (byte 69), covering the list specified by the previous answer.

Normally, Retina takes patterns and replacements in a single file separated by newlines, but we don't have newlines available. Fortunately, Retina 0.8.2 still makes available the language's original multi-file code format.* This program has two stages, a replacement stage and a count stage:

Find all regex matches of _*_*_*_*_*_* in the input, where _ represents the various unprintable characters. Since the input is empty, this matches once. Replace that match with EEEEEE.
In the resulting string, count the number of matches of E (six).

* IIRC, Retina was originally designed this way to take advantage of a PPCG scoring loophole. Now I'm using it to take advantage of a different kind of loophole. Seems appropriate.

The next answer may use the 54 bytes whose codepoints are prime numbers:
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251