Coalesce multiple rows into a comma-delimited value during Update

I have a temporary table with a field called Method, thus:

DECLARE @CaseSites TABLE (
 BriefID  int,
 Method  varchar(60)
 -- other fields
)

Method will be filled from several rows in another table - CaseEventTypeList.

Running

SELECT * FROM CaseEventTypeList WHERE RefID = 1

Gives

RefID TypeID
1  2
1  3
1  6

Turning this into a single comma delimited result is fairly trivial:

DECLARE @CETList varchar(30)

SELECT @CETList = COALESCE(@CETList + ',', '') + CAST(CETL.[TypeID] AS varchar)
FROM CaseEventTypeList CETL 
WHERE CETL.RefID = 1

PRINT @CETList

Giving:

2,3,6

Now I need to expand this to take in the entire table. This is what I came up with:

UPDATE @CaseSites SET Method = COALESCE(Method + ',','') + CAST(CETL.TypeID AS VARCHAR)
 FROM CaseEvents CE
   JOIN CaseEventTypeList AS CETL ON CETL.RefID = CE.TypeListID
 WHERE BriefID = CE.CaseID

However this only fills Method with the first value from each set of values.

I looked online and found this but would rather not use a udf - especially when the solution feels so close.

UPDATE: The data is fairly simple, the RefId is incremented for each case, the TypeID can be any number, though only 1 to 8 are modelled currently. Thus you might have:

RefID TypeID
12  2
12  7
13  1
14  1
14  3
14  6

And this will hopefully be modelled as

SELECT Method from @CaseSites
Method 
...
12  2,7
13  1
14  1,3,6
...