Thanks to advice from Mitch Sun of Blue
Packet, I fixed the problem with the Mark XII electronics! I didn't
realize that a pull-down on a diagnostic serial input was required.
Soldered an additional 10K resistor onto the board, and it's working fine.
"hcitool scan" prints this:
00:12:A1:61:0E:21 BluePacket Bluetooth Wireless Keyboard
Now to design a PC board appropriate for the product!