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Hi Colin,
Do you know if the time base speeds of A and B correspond to those indicated on the knobs? Did you try observing waveforms with both A and B? I'm thinking you may have made an assembly error: The max. A and B rotation and the freedom of rotation angles between A and B are mechanically limited by the knob assembly.

There is a less-intense portion which can be moved by the "Delay Time Position" control, but it's length isn't controlled by the setting of the
B (delayed) time-base knob, only it's position.

I have no idea how familiar you are with this model and 'scopes in general so please don't be insulted if you know all this: Just to make sure we're talking about the same thing, the smaller, grey knob controls the speed of the B timebase, the clear part behind it controls the A time base. The Delay Time knob controls the time after A's start until B starts. If all is well (assembled), A can never be faster than B.

...no bright-up indicating where the B (delayed) time-base will run from and to

This makes me think we are talking about the same A's and B's but the bright-up should be there.

...it's length isn't controlled by the setting of the B (delayed) time-base knob, only it's position.

That sounds strange: The B (delayed) time base knob (the smaller grey one) should control the length of B on A and not influence the starting position.
Sounds like assembly error.

Check the speeds of "A" and "B" relating to the indications on the time scale by applying a signal and see if they make sense.

Raymond