Peachy! So we've determined that the TVT itself works fine. We can set that to one side and concentrate on the keyboard without having it attached to the TVT, which is exactly what we want to do. Divide and conquer.
So, if you have the keyboard on its own power source without the TVT, you should be able to read each keycode on on the output as long as a key is depressed.
Thus, pressing ">", would yield lows on bits 6 and 7 and 1, with all the other outputs high. We'll tackle the KEYPRESSED strobe later. You ant to run through as many keys as you have and verify the output. e.g. Pressing the space bar (and leaving it depressed while you check) should give all outputs low, but for bit 6. With no keys pressed, I think all outputs should be high.
(One confusing thing here is that SWTPC numbers bits from 1, not 0, as would be normal practice.