When I click on the clip the down arrow does reappear, but it does not allow me to select another sequence with different begin and end points. If I select a begin piont which is later than the end of the initial sequence the red begin button reamins greyed out and inactive. The only thing it will let me do is adjust the beginning and ending points of the initial sequence. Somehow it seems that initial sequence needs to be "deselected" so that other sequences can be created, but I see no way to do that.
Update: Okay, I got it. One needs tto move the end point first, and then the begin point, so that the begin point is being selected at a time earlier than the end, even though you're starting a new sequence. Selecting the end before the beginning is not very intuitive, but it makes sense from a computed calculating standpoint.