I have the 2500 but the user manual covers the 1600 as well. I can scan and email (its down on the boat but will bring it back this weekend) - if this is suitable then PM me your email address otherwise I can print and post it.
I've just bought a boat which also has an old Tillerpilot 1600 but no manual. If you have an electronic copy any chance of emailing it? I can't find any more official source.