Assuming that the start timestamp is always identical to the run timestamp, matching the run to the start is a simple join. To find the EndTime, you can use the CROSS APPLY(SELECT TOP 1 ... ORDER BY ...) pattern to locate the next end time following the start.

SELECT R.RunID, S.Timestamp AS StartTime, E.Timestamp AS EndTime
FROM Run R
JOIN TagHistory S
    ON S.timestamp = R.Timestamp
    AND S.Tagname = 'RUNNING'
    AND S.Value = 1
CROSS APPLY (
    SELECT TOP 1 *
    FROM TagHistory E
    WHERE E.timestamp >= S.Timestamp
    AND E.Tagname = 'RUNNING'
    AND E.Value = 0
    ORDER BY E.Timestamp
) E
ORDER BY R.Timestamp

Since you don’t really pull any other data from the start time row, that join can actually be eliminated.

SELECT R.RunID, R.Timestamp AS [StartTime(RunTime)], E.Timestamp AS EndTime
FROM Run R
CROSS APPLY (
    SELECT TOP 1 *
    FROM TagHistory E
    WHERE E.timestamp >= R.Timestamp
    AND E.Tagname = 'RUNNING'
    AND E.Value = 0
    ORDER BY E.Timestamp
) E
ORDER BY R.Timestamp

However, if there is a chance that the start time can be slightly later than the run timestamp (possible with two separate inserts each with its own GETDATE() reference), it would be more reliable to use the CROSS APPLY technique to retrieve both the start and end timestamp rows.

Also, if there is a chance that one or both history rows might be missing (perhaps a job is still running), changing the CROSS APPLY to an OUTER APPLY will still yield a result rows (similar to a LEFT JOIN.

SELECT
    R.RunID, R.Timestamp as RunIdTime,
    S.Timestamp AS StartTime, E.Timestamp AS EndTime
FROM Run R
OUTER APPLY (
    SELECT TOP 1 *
    FROM TagHistory S
    WHERE S.timestamp >= R.Timestamp
    AND S.Tagname = 'RUNNING'
    AND S.Value = 1
    ORDER BY S.Timestamp
) S
OUTER APPLY (
    SELECT TOP 1 *
    FROM TagHistory E
    WHERE E.timestamp >= S.Timestamp
    AND E.Tagname = 'RUNNING'
    AND E.Value = 0
    ORDER BY E.Timestamp
) E
ORDER BY R.Timestamp

The above queries assume that the timestamp values do not have ambiguities, such as duplicate run timestamps, overlapping runs, or one run’s end timestamp equaling the next run’s start time.

Sample results (with some extra data):

See this db<>fiddle for a demo.