SQL: Grouping Paired Rows Without Field to Aggregate On

As having a DBMS containing window function, you can use the following query

WITH t AS
( 
  SELECT CASE
           WHEN Event_Name = 'SUSPEND' THEN
            Timestamp
         END AS Suspend,
         CASE
           WHEN Event_Name = 'RESUME' THEN
            Timestamp
         END AS Resume,
         SUM(CASE
               WHEN Event_Name = 'SUSPEND' THEN
                1
               ELSE
                0
             END) OVER(PARTITION BY Event_Name ORDER BY Timestamp) AS rn_suspend,
         SUM(CASE
               WHEN Event_Name = 'RESUME' THEN
                1
               ELSE
                0
             END) OVER(PARTITION BY Event_Name ORDER BY Timestamp) AS rn_resume  
    FROM t
)
SELECT s.suspend, r.resume
  FROM (SELECT * FROM t WHERE resume IS NOT NULL) AS r
  FULL JOIN (SELECT * FROM t WHERE suspend IS NOT NULL) AS s
    ON s.rn_suspend = r.rn_resume
 ORDER BY r.rn_resume DESC, s.rn_suspend DESC

where SUM window function is used to count the each switch for the Event_Name

Demo