Great question, and easy answer.
S-VHS VCR TBC = line TBC
external TBC = frame TBC ----- and referring specifically to the Cypress/DataVideo type TBCs we use for analog videotape sources (not broadcast TBCs, etc -- those are not the same whatsoever)
Line TBC cleans the image,
Frame TBC cleans the signal.
You need both TBCs.
Line TBC is intraframe, X*Y axis
Frame TBC is interframe/temporal, Z axis
Video is X*Y*Z (length x width x time)
Without frame TBC, the signal is erratic, so dropped frames and audio sync issues are likely.
It's actually more complicated than this, but the basic geometry/algebra equations are digestible fior those who are new to video. And honestly, unless you're trying to develop hardware/software to process video, that explanation should suffice forever, for almost all people.
Now then.... stacking TBCs question...
The only time that stacked TBCs get ignored is when the functions are alike. So line>line duplicates, and frame>frame duplicates, but line>frame does not.
However, do note that frame>line is not possible, the frame correction bakes in line errors. So line must be first in a stack.
As a primary example, The ES10/15 DVD recorder (not a TBC!) contains a strong+crippled line TBC, with non-TBC frame sync, and it has many quality-reducing issues. Those are ideally used only when the net effect of its strong TBC + harmed quality = net better video.
Net better, not absolute better. For example:
bad + bad = bad
good + bad = neutral (to bad)
excellent + bad(ish) = good = "net better"
The ES10/15 strong line can be excellent, the rest of the unit processing is pretty craptastic/bad(ish).
When you put a ES10/15 behind a regular VHS VCR, you get some corrections, but then you also get all the "muck" of the low-end VCRs, combined with the DVD recorder. It's better than nothing, but don't fool yourself into thinking it's "best", and "good enough" is an excuse to accept lesser quality.
When you put ES10/15 behind S-VHS VCR, you get the benefits of the S-VHS, but the downsides of the DVD recorder. When the VCR TBC is on, the DVD recorder line TBC literally does nothing. It's inert, it cannot make any corrections to the already-correct signal. In fact, it often makes quality worse, as it attempts to "correct" an already-corrected signal. The non-TBC frame sync doesn't do much, maybe baking in the "Z axis" data to a force clock (non corrective).
So the only way to make an ES10/15 work behind a S-VHS VCR is to disable the VCR TBC, or just use a non-TBC S-VHS VCR. Not that you should.
Even with the non-TBC frame sync, the output from ES10/15 can still be mistimed temporally, and you'll get dropped frames. So you want to chase it with an actual frame TBC, even if it's just a weaker TBC(ish) like a modded DVK, or the "also has" frame TBC devices (but noting all of those have side effects as well, especially non-DVK units). When you put regular VCR, ES10/15 strong+crippled line DVD recorder, non-TBC "also has" weak frame TBC device, into a single workflow, you're basically covering your video under a layer of garbage. Granted, it's better garbage than "nothing at all" (ie, cheap VCR into pathetic Chinese USB capture card or HDMI converter junk), but it's still added garbage/artifacts/etc.
So does that make sense?
VCR > some form of TBC > capture card is the most basic formula for video. But it shouldn't just be any random VCR, TBC, capture card. When you use a specific formula of
JVC/Panasonic S-VHS VCR with line TBC > DataVideo/Cypress type frame TBC > ATI/Pinnacle type capture card, then you're operating a level to get clean quality video. Errors removed, nothing really added.