SQL Server 2019

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WITH chr AS (
    SELECT 581827 AS custno, '2012-11-08 08:38:00.000' AS moddate, 'EMSZC14' AS who UNION ALL
    SELECT 581827, '2012-11-08 08:41:10.000', 'EMSZC14' UNION ALL
    SELECT 581827, '2012-11-08 08:53:46.000', 'EMSZC14' UNION ALL
    SELECT 581827, '2012-11-08 08:57:04.000', 'EMSZC14' UNION ALL
    SELECT 581827, '2012-11-08 08:58:35.000', 'EMSZC14' UNION ALL
    SELECT 581827, '2012-11-08 08:59:13.000', 'EMSZC14' UNION ALL
    SELECT 581827, '2012-11-08 09:00:06.000', 'EMSZC14' UNION ALL
    SELECT 581827, '2012-11-08 09:04:39.000', 'EMSZC49' UNION ALL  -- Reset row number to 1
    SELECT 581827, '2012-11-08 09:05:04.000', 'EMSZC49' UNION ALL
    SELECT 581827, '2012-11-08 09:06:32.000', 'EMSZC49' UNION ALL
    SELECT 581827, '2012-11-08 09:12:03.000', 'EMSZC49' UNION ALL
    SELECT 581827, '2012-11-08 09:12:38.000', 'EMSZC49' UNION ALL
    SELECT 581827, '2012-11-08 09:14:18.000', 'EMSZC49' UNION ALL
    SELECT 581827, '2012-11-08 09:17:35.000', 'EMSZC14' UNION ALL  -- Reset row number to 1
    SELECT 581829, '2012-11-08 09:12:03.000', 'EMSZC14' UNION ALL  -- 1
    SELECT 581829, '2012-11-08 09:12:38.000', 'EMSZC49' UNION ALL  -- 1
    SELECT 581829, '2012-11-08 09:14:18.000', 'EMSZC49' UNION ALL
    SELECT 581829, '2012-11-08 09:17:35.000', 'EMSZC14'            -- Reset row number to 1
),
cte AS (
    SELECT *,
        ROW_NUMBER() OVER (PARTITION BY custno ORDER BY moddate) rn1,
        ROW_NUMBER() OVER (PARTITION BY custno, who ORDER BY moddate) rn2
    FROM chr
)

SELECT custno, moddate, who,
    ROW_NUMBER() OVER (PARTITION BY custno, rn1 - rn2 ORDER BY moddate) rn
FROM cte
ORDER BY
    custno,
    moddate;

custno	moddate	who	rn
581827	2012-11-08 08:38:00.000	EMSZC14	1
581827	2012-11-08 08:41:10.000	EMSZC14	2
581827	2012-11-08 08:53:46.000	EMSZC14	3
581827	2012-11-08 08:57:04.000	EMSZC14	4
581827	2012-11-08 08:58:35.000	EMSZC14	5
581827	2012-11-08 08:59:13.000	EMSZC14	6
581827	2012-11-08 09:00:06.000	EMSZC14	7
581827	2012-11-08 09:04:39.000	EMSZC49	1
581827	2012-11-08 09:05:04.000	EMSZC49	2
581827	2012-11-08 09:06:32.000	EMSZC49	3
581827	2012-11-08 09:12:03.000	EMSZC49	4
581827	2012-11-08 09:12:38.000	EMSZC49	5
581827	2012-11-08 09:14:18.000	EMSZC49	6
581827	2012-11-08 09:17:35.000	EMSZC14	1
581829	2012-11-08 09:12:03.000	EMSZC14	1
581829	2012-11-08 09:12:38.000	EMSZC49	1
581829	2012-11-08 09:14:18.000	EMSZC49	2
581829	2012-11-08 09:17:35.000	EMSZC14	1