There are however many grey areas, if you look at Chapter 33 in the Syllabus you'll notice that it's Level 3 for B2. B1 isn't listed for that Chapter, yet not many line B1's who won't change a lamp.
From the UK CAA's ELGD (Engineers Licence Guidance Document)
The B1 licence is a mechanical based licence and
permits the holder to issue certificates of release to
service following line maintenance, including aircraft
structure, power plants and mechanical and electrical
systems. Replacement of avionic line replaceable units
requiring simple tests without the use of test equipment
to prove their serviceability is also included within the
privileges of this licence. A Category B1 licence holder
also has a role in base maintenance in supporting the
Category C certifier who is the final CRS/SMI signatory.
This would suggest that Chapter 33 is indeed covered if a "simple" test can be actioned without the use of test equipment.
What do your quality department say a B1 can cover?