Here's another link for you
AMC ED 2003/19 Acceptable Means of Compliance.
The section in question is worded thus
3. The category B1 licence also permits the certification of work involving avionic
systems, providing the serviceability of the system can be established by a simple
self-test facility, other on-board test systems/equipment or by simple ramp test
equipment. Defect rectification involving test equipment which requires an element of
decision making in its application - other than a simple go/no-go decision - cannot be
certified.
Page 248.
That reads to me that a B1 could do the deed on something like a modern Airbus where no test equipment is needed and you just answer a series of yes/no questions on the CMC/CFDS. If it were a DC10 or classic Jumbo then the same could not be said.
Company procedures will dictate who is allowed to upgrade an Autopilot and under what circumstances. I've worked at places where the Autopilot could not be upgraded until the Tech Services department reviewed the history and work actioned and issued a work order to test and then upgrade if the test was ok.
Other firms were more lax and allowed the individual B2 to decide if the upgrade is warranted.
EASA seem to leave it to the operator to put a system in place and give certification privileges as above allowing a B1 to certify so long as the criteria are met.
Some of our customers are very cautious and request MCC contact before deferring anything - an autopilot upgrade without contacting them even by an experienced B2 would result in lots of s**t hitting the fan.
All you can do really is contact the quality department and ask for guidance.