When either of the three switches are turned on, check status of all three switches. If only one switch is now on create a new record and log the time stamp the switch was turned on. Do nothing if a switch is already on (2 or more switches are now on).
When a switch is turned off, count the number of on switches again. If no switches are now on, log the timestamp out in a second field of the same record. If at least one other switch is still on, do nothing.
The sum of the differences of your on and off times divided by sixty will count the minutes at least one switch is on.
Perfect! Now a switch has turned on in my brain, too. Thanks.