This is way off topic for me, but let me try to help you a bit.
You've seen several instances of the word "SYNC" that should be, for all practical purposes, isolated. The "SYNC" position of the monitor switches changes the monitor source from the playback head to the record head, so that a new recording made while listening to other tracks being played back will come back in "sync" with the other tracks.
Th SYNCLOCK input is essential in syncing the machine, but is not, in and of itself, a synchronizer. In your case, you would require an external box that compares the SMPTE code that you're going to record (on one track of your 16 track) to the SMPTE code that's output by your DAW; this box then corrects the position of the analog machine such that it comes up "in sync" to the reference input (the DAW) - sometimes this requires a minute adjustment of the capstan speed, thus an external phase lock input.
Beyond that, I don't know who makes this Tascam-compatible synchronizer anymore, especially who makes one cheaply.
There must be someplace else to post this question - have you tried rec.audio.pro?