SQL Server 2019

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CREATE TABLE ELIGIBILITY ( EFF_DT DATETIME,
                           TERM_DT DATETIME,
                           ID1 INT,
                           ID2 INT );

INSERT INTO ELIGIBILITY (EFF_DT, TERM_DT, ID1, ID2) VALUES
('25 MAY 1990','30 NOV 1994',18,36), -- 1 DAY GAP 
('01 DEC 1994','31 DEC 1994',18,36), -- 1 DAY GAP
('01 JAN 1995','11 FEB 1995',18,36), -- 1 DAY GAP
('05 APR 1995', '31, DEC 1995',18,36), -- 53 DAY GAP
('16 JUN 2002','20 APR 2007',18,36), -- 2539 DAY GAP
('16 JUN 2002','20 APR 2007',12,3),
('21 JUL 2007','28 JUL 2007',12,3), -- 92 DAY GAP
('08 AUG 2007','31 AUG 2007',12,3), -- 11 DAY GAP
('11 OCT 2007','31 DEC 2007',12,3), -- 41 DAY GAP
('01 JAN 2008','07 JAN 2008',12,3), -- 1 DAY GAP
('14 JAN 2008','21 JAN 2008',12,3), -- 7 DAY GAP
('01 JUN 2008','30 SEP 2008',12,3), -- 5 MONTH GAP
('31 OCT 2008','30 NOV 2008',12,3), -- 30 DAY GAP
('01 JAN 2009','31 JAN 2009',12,3), -- 31 DAY GAP
('04 MAR 2009','31 MAR 2009',12,3), -- 32 DAY GAP
('03 MAY 2009','31 MAY 2009',12,3), -- 33 DAY GAP
('04 JUL 2009','31 JUL 2009',12,3);  -- 34 DAY GAP

SELECT * FROM ELIGIBILITY;

EFF_DT	TERM_DT	ID1	ID2
1990-05-25 00:00:00.000	1994-11-30 00:00:00.000	18	36
1994-12-01 00:00:00.000	1994-12-31 00:00:00.000	18	36
1995-01-01 00:00:00.000	1995-02-11 00:00:00.000	18	36
1995-04-05 00:00:00.000	1995-12-31 00:00:00.000	18	36
2002-06-16 00:00:00.000	2007-04-20 00:00:00.000	18	36
2002-06-16 00:00:00.000	2007-04-20 00:00:00.000	12	3
2007-07-21 00:00:00.000	2007-07-28 00:00:00.000	12	3
2007-08-08 00:00:00.000	2007-08-31 00:00:00.000	12	3
2007-10-11 00:00:00.000	2007-12-31 00:00:00.000	12	3
2008-01-01 00:00:00.000	2008-01-07 00:00:00.000	12	3
2008-01-14 00:00:00.000	2008-01-21 00:00:00.000	12	3
2008-06-01 00:00:00.000	2008-09-30 00:00:00.000	12	3
2008-10-31 00:00:00.000	2008-11-30 00:00:00.000	12	3
2009-01-01 00:00:00.000	2009-01-31 00:00:00.000	12	3
2009-03-04 00:00:00.000	2009-03-31 00:00:00.000	12	3
2009-05-03 00:00:00.000	2009-05-31 00:00:00.000	12	3
2009-07-04 00:00:00.000	2009-07-31 00:00:00.000	12	3

WITH
CTE1 AS (SELECT LAG(TERM_DT) OVER (PARTITION BY ID1,ID2 ORDER BY EFF_DT) PREV_DT,
                EFF_DT,
                TERM_DT,
                LEAD(EFF_DT) OVER (PARTITION BY ID1,ID2 ORDER BY EFF_DT) NEXT_DT,
                ID1, 
                ID2
         FROM ELIGIBILITY),
CTE2 AS (SELECT EFF_DT,
                TERM_DT,
                ID1, 
                ID2, 
                COALESCE(DATEDIFF( DAY, PREV_DT, EFF_DT), 1000) D1, 
                COALESCE(DATEDIFF(DAY, TERM_DT, NEXT_DT), 1000) D2
         FROM CTE1
         WHERE COALESCE(DATEDIFF( DAY, PREV_DT, EFF_DT), 1000) > 63 
            OR COALESCE(DATEDIFF(DAY, TERM_DT, NEXT_DT), 1000) > 63)
SELECT DISTINCT
       CASE WHEN D1 > 63 
            THEN EFF_DT
            ELSE LAG(EFF_DT) OVER (PARTITION BY ID1,ID2 ORDER BY EFF_DT) 
            END EFF_DT,
       CASE WHEN D2 > 63 
            THEN TERM_DT
            ELSE LEAD(TERM_DT) OVER (PARTITION BY ID1,ID2 ORDER BY EFF_DT) 
            END TERM_DT,
       ID1,
       ID2
FROM CTE2
ORDER BY ID1, ID2, EFF_DT

EFF_DT	TERM_DT	ID1	ID2
2002-06-16 00:00:00.000	2007-04-20 00:00:00.000	12	3
2007-07-21 00:00:00.000	2008-01-21 00:00:00.000	12	3
2008-06-01 00:00:00.000	2009-07-31 00:00:00.000	12	3
1990-05-25 00:00:00.000	1995-12-31 00:00:00.000	18	36
2002-06-16 00:00:00.000	2007-04-20 00:00:00.000	18	36