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Track state of time series event in SQL column

This seems really simple but I can’t figure it out, working in SQL Server. I have time series data and I want a column to track the state of ON/OFF events for each row, so when there’s an ON event then the Desired Output column will have a 1 for each subsequent event until there is an OFF event. Please see example below. Thanks so much!

TimeStamp Event Desired Output
1:01 ON 1
1:02 OFF 0
1:04 other 0
1:05 other 0
1:06 ON 1
1:10 other 1
1:12 other 1
1:14 OFF 0
1:15 other 0

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