What are the specifications of the paper used in drywall/gypsum board?

I don't have those specifications.  Perhaps another researcher will be
able to help you... I've asked the editors to remove my answer.

ASTM has an "ACTIVE STANDARD: C1396/C1396M-04 Standard Specification
for Gypsum Board" for sale at $34.

I can't tell if it covers the paper used, but you can contact their
customer service center for "more information about an ASTM standard
or product." The customer service center has a toll number and an
email address listed on:

http://www.astm.org/cgi-bin/SoftCart.exe/SUPPORT/index.html?L+mystore+yxys4506+1145419959

A description of the standard is at:

http://www.astm.org/cgi-bin/SoftCart.exe/DATABASE.CART/REDLINE_PAGES/C1396C1396M.htm?L+mystore+yxys4506+1145419830

This current standard consolidates nine gypsum board standards:

http://www.astm.org/cgi-bin/SoftCart.exe/SNEWS/DECEMBER_2004/gypsum_dec04.html?L+mystore+vkmf4721

Search strategy:
"paper specifications" ~drywall "gypsum board"
astm ~drywall "gypsum board"

then a search at astm.org