Caulking at base of unstable fiberglass shower wall

That tape won't stick to soap scum. Gotta wipe the plastic down with whatever solvent works before you apply it. I would not use it for that application anyway. As much as people hate silicone caulk, it is about the only thing that will hold up for that application. You may need to stuff the joint with some backer rod of some kind before you apply it, like oakum on an old leaded joint.

What's behind the problem wall? Are we talking a "standalone" cubicle, or are the panels mounted onto something more solid? We've got crappy[1] panels around our shower too, mounted onto drywall, and the only solution was to pull them down and fit something structural behind them before putting them back up - why this was never done in the first place, I don't know, but they'd flex at the bottom and split caulk seams, too. Packing them out with some 1/4" strips nailed to the drywall worked well.

cheers

Jules

If the excellent suggestions above don't get it done, bite the bullet and get a decent shower assembly from a major manufacturer and install it better than your present one. The shower is probably not the only hack job around your house so that will give you time to get on with other surprises that will pop up.

Joe