Actions don't work that way. An Action is tied to a specific viz: that's the lowest level of control we have over the behavior when you initiate the Action. You can't have different actions based on different parts of the same viz.
The usual solution is to build multiple vizzes and place them on your dashboard so that they LOOK like one viz to the user, and have different Actions for the different vizzes.
So in your case, you have a worksheet for the bar graph that leads to sheet 1, and a different worksheet for the bar graph that leads to sheet 2, and you create 2 actions, one for each worksheet.
I don't know of a way to do that at the bar SEGMENT level, though.
Use the filter action with menu selection and create two filters here. one for sheet 1 and another for sheet 2.
user can select the bar and get action name in tooltip and they can choose where they want to go.
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Michael's comment about Filter actions is correct but if you switch to URL actions you can make them dynamic and even hidden for some bar segments. If the URL for a URL action references a field in the viz, and the field is null, the URL action will not be shown in the tooltip. That's how you can hide actions that don't apply (or aren't allowed to be run by the logged-in user). You can pass filter values through the URL so they work like Filter actions. See the following demo, I implemented the two URL actions differently to show different levels of self-referencing (same server vs. same workbook).
Thanks, Zach. Your approach looks manageable for me. I will then switch to URL actions.