Managed to find the solution a similar solution in "STACK OVER FLOW" and then had to modify it slightly. So it works .. Here you go 


;WITH T AS
(
SELECT *,
   DENSE_RANK() OVER (ORDER BY EligMonth) - EligMonth AS Grp
FROM #t
),
CONSECUTIVE_MONTHS_TOGETHER as
(
SELECT
     BeneficiaryID,
     MIN(EligMonth) AS RangeStart,
   MAX(EligMonth) AS RangeEnd,
     MAX(EligMonth) - MIN(EligMonth) as DIFF
FROM T
GROUP BY BeneficiaryID, Grp
)
Select * FROM CONSECUTIVE_MONTHS_TOGETHER WHERE DIFF > 2 --( See Explanation )

/*
This solution works when the numbers are in a sequence ( that is the case with my example )
So if you had any 3 months of consecutive coverage the difference between the largest and smallest must be > 2 -- OR ( >= (3) )
*/


Here is the internet article that helped me....

https://stackoverflow.com/questions/7608370/how-can-i-check-a-group-of-numbers-are-consecutive-in-t-sql


CASE CLOSED ... NO FURTHER HELP NEEDED. Have a wonderful day .