GROUP BY causes NativeError: [10053]

This indicates that GROUP BY is to slow to answer in time.

If the selectivity of field1 is very low this may take quite a while.
The closer field1 is to unique the longer it takes as it produces a large resultset.

You may allow a longer timeout. But pls. don't ask me how. Some other experts may know. 

If your GCT.PA_Data is a huge thing you may slice it into pieces by year, id,  ... whatever seems useful:

Example:

SELECT field1 F1, count(field2) CntF2
FROM (
     SELECT filed1,field2 from GCT.PA_Data
     where field1 is not null and ID between 1 and 100000
) group by field1

This is not the final solution but a way to understand the limits of your server.

BTW:
an index on field1 might be useful anyhow
Example

Index ff on field1 [ DATA = filed2 ] ;

with this construct, your query will only access this special index
instead of the full record and NULL fields are all grouped in advance.

It is kind of a "materialized view" that other DBs offer.

Groran, to make sure that problem is the connection timeout you can test the SQL in terminal. Terminal connection doesn't have timeout. and you can see how much it costs. Here is example from documentation:

SAMPLES>SET result=$SYSTEM.SQL.Execute("SELECT TOP 5 name,dob,ssn FROM Sample.Person")

SAMPLES>DO result.%Display()