Does handlebar tape go inside the bar, under the bar-end shifter, when using bar-end shifters? I'm installing bar-end shifters for the first time (Shimano 9-speeds, for what it's worth) and was wondering if I should be running the tape over the bottom of the handlebar with surplus to insert into the bar.  In the past, I've done this and used wine corks or handlebar caps to hold the tape in.  When using cloth tape, this is no problem; foam/cork tape usually is fine too.  But is it the same with bar-end shifters?
Most bar-end shifters require friction between the bar's interior surface to stay put, so no. Install the shifters securely and tape the shifter housing about where you would like it to emerge from the bar tape. You will end up wrapping over the first few inches of shifter housing before it loops forward and may require a bit of futzing to get it looking right.

Here is a lovely video showing shifters being installed on a drop bar.