Actually, *this* might be my final question. I've seen people talk about external units like the TimeLine you mention for sync capabilities. What exactly would I need in order to slave a 388 or TSR-8 to a DAW?
You have a choice as to how you want to connect the tape machine to the synchronizer, and how you want to connect the computer to the synchronizer.
The tape machine can be driven in one of two ways: Serial, via the accessory-2 port, or Parallel via the Accessory-1 port. For the most part, only TASCAM synchronizers are liable to be able to use the serial protocol.
Parallel protocol is more standard, but there are various per-manufacturer quirks about whether it's positive or negatively triggered, whether the capstan speed is voltage-controlled or frequency-controlled, what the clock frequency should be and things like that.
These settings will be controlled electronically by the synchronizer (though you will probably need a different cable for each deck type). The Lynx MK1 is parallel only, I don't know about the Lynx II or MicroLynx.
The ATS-500 uses TASCAM's serial protocol, though there is an optional add-on, the IF/500 to allow it to talk to parallel decks too.
The MTS1000 Midiizer uses serial, I'm not sure if it supports parallel mode.
Now, the computer side of things. Basically you have two more choices here. If you have a synchronizer that can lock a tape deck against a MIDI MTC code, that's great. There aren't many of those, though - the MicroLynx might be the only one. I thought the TASCAM MMC100 could do this, but unfortunately I was wrong. It can control the deck and force it to start under MIDI control but it will not regulate the speed of the deck.
For the most part, synchronizers of this kind are designed to make two tape decks lock together, or lock a tape machine against a video deck. They will expect a timecode incoming from the master deck, and optionally control signals as well, though it is possible to do a timecode-only lock.
What you would do is record timecode on the DAW, and feed that in is the master timecode. Then it should make the slave deck chase that (for best results on the ATS500, enable both CHASE and PHASE modes).
EDIT: I was going to add that with the Lynx MK1, you have to have one for each deck. I was also going to point out that with the manual, with all the cables and months of trying, I never did manage to get the Lynx to slave the machines properly. They make very nice dual timecode monitors, though.