Let me see if I can say it properly:
When you run StartToaster, the Toaster genlocks the Amiga to the video source at input 1. If you lose that video source at any time after that, you're done.
The time base corrector does at least two things. It replaces the sync signals with its own, which are very clean and stable. Second, it genlocks one video source to another, namely, whatever you ultimately send to two inputs on the Toaster. It probably also cleans up the video (many do).
If you have a dual TBC, like the Kitchen Sync (if you buy a TBC, do buy one of these if you can), it genlocks its input B to its Input C and optionally to a third source, usually another TBC.
If you only have two video sources, and at least one is very stable, plug that one into both video input 1 on the Toaster, and the auxiliary in on a single TBC. Then plug your second video source into the single TBCs video input. Plug the TBC output into input 2 on the Toaster.
If you have a dual TBC, you can either have three video sources, or just plug your two into both inputs on the TBC, and plug both outputs into inputs 1 and either 2,3, or 4 (preferably 2, especially if you have a Flyer) on the Toaster. For more sources, you do the same as you would for two sources with a single TBC.
If a video source is anything but a camera (and even if it is a camera in some cases) it cannot be plugged directly into the Toaster in any case, it must be run through a TBC. VCRs and computers especially, usually also DVD and CED players. Laser Disc players fall into the camera category: most work, some don't. Even then, it can depend on the disc.