I think your mechanic is probably referring to the crankshaft sensor.
That would be consistent with what you describe as well as the
mechanic’s thoughts about the water pump and the timing belt.  The
engine doesn’t need to be removed, but all the items necessary to
reach the timing belt do.  

If you haven’t yet replaced the timing belt, don’t hesitate to do this
repair.  This engine has been known to have premature timing belt
failures, so I recommend at least strict adherence to the schedule for
replacing the timing belt and balance shaft belt, which is every 4
years or 60,000 miles, whichever comes first.  Given your symptoms,
this is also the time to replace the sensor.  

The water pump is another issue.  They don’t fail all that often, but
with the timing belt off it’s only a small amount of additional labor
to replace.  On the other hand, if it fails later, it’ll be a
significant amount of labor just to access the water pump again.
There are differing philosophies here, and you’ll need to pick your
poison