Thanks for the tips
I tried this using just one live camera, a VCR, and one TBC. (I only have one live camera.)
I used an RCA y-cable from RadioShack to split the camera's output, and connected the y-cable to the TBC's genlock input and to the Video Toaster's input 1. I connected the VCR to the TBC's video input. I connected the TBC's video output to the Video Toaster's input 2.
No change
I'm starting to suspect that I either have a fundamental misunderstanding of this process, or that the TBCs are bad (even though the seller listed them as working).
Anyone else have any ideas?