I agree that A12.32 only mentions movement as being prohibited for HIP units, but the following Q&A implies that HIP units may not perform any action, although it does not address the issue directly.
A12.14 & A12.3
May a hidden unit not in enemy LOS voluntarily sacrifice its hidden status, and become concealed in order to perform some action (e.g., Deploy during the RPh, Entrench during the PFPh, Place SMOKE during the MPh, voluntarily break a MMC in order to rout with a still concealed/hidden leader, transfer a weapon during the APh, etc.), or to undertake no activity at all during that phase? Or is the unit “totally discovered” the moment it sacrifices its hidden status under these circumstances? May a hidden unit in enemy LOS voluntarily sacrifice its hidden status, and become concealed in order to perform a non-concealment loss activity, or no activity at all during that phase? Or is the unit “totally discovered” the moment it sacrifices its hidden status under these circumstances? A. The former in both cases.